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This document discusses similar solids and provides definitions, theorems, and examples. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. The Similar Solids Theorem states that if two similar solids have a scale factor of a:b, then their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. The document provides homework problems for students to practice applying these concepts of similar solids.
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5.1 5.2 notes
This document discusses midsegments and perpendicular bisectors of triangles. It defines a midsegment as a segment connecting the midpoints of two sides of a triangle, and states that every triangle has three midsegments that are parallel to the opposite side and half as long. It also defines a perpendicular bisector as a line perpendicular to a segment at its midpoint, and explains that all points on the bisector are equidistant from the endpoints. Additionally, it introduces the circumcenter as the point where the three perpendicular bisectors of a triangle intersect.
1.9 notes
This document contains notes from a math lesson on multiplying and dividing integers:
1) It provides rules for multiplying integers based on the signs of the numbers, and examples of multiplying integers.
2) It then provides rules for dividing integers based on the signs of the numbers, and examples of dividing integers.
3) The final page lists homework problems assigning students to complete selected even problems from page 47 and problems 61-65.
3.1 notes
This document contains notes for homework on solving systems by graphing. It lists the homework problems as problems 3 through 39 on page 128, with the topic being multiples of 3. The notes were created on September 19, 2014.
10.3 notes
The document outlines a geometry lesson on the properties of chords that took place on February 15, 2012. It divides students into four groups to focus on Theorems 10.3 through 10.6, and includes bellwork, learning objectives, and homework assignments.
1.4 notes
This document discusses measuring and classifying angles. It defines an angle as being formed by two rays with a common endpoint. Angles are measured using a protractor and can be acute (<90 degrees), right (90 degrees), obtuse (>90 degrees but <180 degrees), or straight (180 degrees). The document also mentions the angle addition postulate and that congruent angles have the same measure.
4.5 notes
This document is a homework worksheet for solving and graphing absolute value inequalities from October 9, 2014. It contains instructions for students to practice solving absolute value inequalities algebraically and graphing the solutions on a number line. The worksheet is repeated multiple times and covers solving and graphing absolute value inequalities as the key topics.
4.7 notes
This document defines and discusses properties of isosceles and equilateral triangles. It states that an isosceles triangle has two sides of equal length, and the angles opposite the equal sides are also equal. Additionally, if two angles of any triangle are equal, then the sides opposite those angles are also equal. If a triangle's three sides are equal in length, it is both equilateral and equiangular. The document also provides an example of finding the measure of an angle in an equilateral triangle.
10.2 notes
This document defines key terms and concepts related to arcs of circles such as central angle, minor arc, major arc, semicircle, and how to calculate arc measures. It introduces the arc addition postulate which states the measure of an arc is equal to the sum of the measures of its interior arcs. Finally, it notes that congruent circles have congruent arcs of the same measure.
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5.1 5.2 notes
This document discusses midsegments and perpendicular bisectors of triangles. It defines a midsegment as a segment connecting the midpoints of two sides of a triangle, and states that every triangle has three midsegments that are parallel to the opposite side and half as long. It also defines a perpendicular bisector as a line perpendicular to a segment at its midpoint, and explains that all points on the bisector are equidistant from the endpoints. Additionally, it introduces the circumcenter as the point where the three perpendicular bisectors of a triangle intersect.
1.9 notes
This document contains notes from a math lesson on multiplying and dividing integers:
1) It provides rules for multiplying integers based on the signs of the numbers, and examples of multiplying integers.
2) It then provides rules for dividing integers based on the signs of the numbers, and examples of dividing integers.
3) The final page lists homework problems assigning students to complete selected even problems from page 47 and problems 61-65.
3.1 notes
This document contains notes for homework on solving systems by graphing. It lists the homework problems as problems 3 through 39 on page 128, with the topic being multiples of 3. The notes were created on September 19, 2014.
10.3 notes
The document outlines a geometry lesson on the properties of chords that took place on February 15, 2012. It divides students into four groups to focus on Theorems 10.3 through 10.6, and includes bellwork, learning objectives, and homework assignments.
1.4 notes
This document discusses measuring and classifying angles. It defines an angle as being formed by two rays with a common endpoint. Angles are measured using a protractor and can be acute (<90 degrees), right (90 degrees), obtuse (>90 degrees but <180 degrees), or straight (180 degrees). The document also mentions the angle addition postulate and that congruent angles have the same measure.
4.5 notes
This document is a homework worksheet for solving and graphing absolute value inequalities from October 9, 2014. It contains instructions for students to practice solving absolute value inequalities algebraically and graphing the solutions on a number line. The worksheet is repeated multiple times and covers solving and graphing absolute value inequalities as the key topics.
4.7 notes
This document defines and discusses properties of isosceles and equilateral triangles. It states that an isosceles triangle has two sides of equal length, and the angles opposite the equal sides are also equal. Additionally, if two angles of any triangle are equal, then the sides opposite those angles are also equal. If a triangle's three sides are equal in length, it is both equilateral and equiangular. The document also provides an example of finding the measure of an angle in an equilateral triangle.
10.2 notes
This document defines key terms and concepts related to arcs of circles such as central angle, minor arc, major arc, semicircle, and how to calculate arc measures. It introduces the arc addition postulate which states the measure of an arc is equal to the sum of the measures of its interior arcs. Finally, it notes that congruent circles have congruent arcs of the same measure.
3.3 notes
This document discusses six theorems for proving that two lines are parallel: (1) the corresponding angles converse theorem, (2) the alternate interior angles converse theorem, (3) the alternate exterior angles converse theorem, (4) the consecutive interior angles converse theorem, (5) using a paragraph proof, and (6) the transitive property of parallel lines theorem. It also assigns homework problems from page 165 involving using these theorems to prove lines are parallel.
5.1 5.2 notes
The document discusses midsegments and perpendicular bisectors of triangles. It states that every triangle has 3 midsegments that are parallel to the sides and half the length. It also explains that the perpendicular bisector of a segment is perpendicular at the midpoint and that any point on the bisector is equidistant from the endpoints. The perpendicular bisectors of a triangle are concurrent at the circumcenter.
3.2 notes
This document discusses parallel lines and transversals. It defines corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It states that if two parallel lines are cut by a transversal, then corresponding angles, alternate interior angles, and alternate exterior angles are congruent. It also states that if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. Students are instructed to complete guided practice problems with a partner.
5.7 notes
This document contains notes about complex numbers from a math class, including the section number, homework page and problem numbers, and date. It repeatedly lists the topic as complex numbers, and references homework problems about multiples of 5.
1.6 notes
The document is from a geometry class and discusses classifying polygons. It defines polygons as closed figures with 3 or more sides where each side intersects exactly 2 other sides. Polygons are named by listing the vertices in order. They can be convex, with no interior points, or concave, with interior points. Common polygons include triangles, quadrilaterals, pentagons, and hexagons. Regular polygons are convex, equilateral, and equiangular. Students are assigned homework problems classifying polygons.
11.5 notes
This document discusses formulas and examples for calculating the areas of circles, sectors, segments, and annuli. It introduces the formula for calculating the area of a circle as πr^2. It then provides examples of using this formula, as well as the formula for calculating the area of a sector, which is (portion of the circle) x (area of the circle). The document concludes by assigning homework problems from page 758 numbers 3 through 31 odds.
1.2 notes
This document defines key concepts about line segments and congruence. It introduces coplanar points, ways to write line segments, and the segment addition postulate which states that if point B lies between points A and C on a line, then the length of AB plus BC equals the length of AC. It also defines congruent segments as line segments with the same length and provides examples of using the segment addition postulate and defining congruent segments. The document assigns homework problems applying these concepts.
2.2 p1 notes
1) The document discusses conditional statements, which are logical statements written in an "if-then" form with a hypothesis and conclusion. Examples of conditional statements and their conversions to inverse, converse, and contrapositive forms are provided.
2) Homework problems are assigned from pages 82 and 83, involving analyzing conditional statements, determining if they are true or false, and identifying definitions as conditional statements.
3) A conditional statement can be written as a biconditional statement using "if and only if" when the conditional statement and its converse are both true. Definitions can also be written as biconditional statements.
4.1 notes
The document contains notes from a geometry lesson that discuss classifying triangles based on their sides and angles. It defines key concepts like the triangle sum theorem, which states that the sum of the interior angles of any triangle is 180 degrees. It also describes the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. Examples are provided to illustrate these theorems.
Trig 2 notes
The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It then gives examples of using the Law of Sines to find specific values like side lengths and triangle areas.
1.4 notes
This document discusses measuring and classifying angles. It defines an angle as being formed by two rays with a common endpoint called the vertex. Angles are measured in degrees using a protractor and are classified as acute (<90°), right (90°), obtuse (>90° and <180°), or straight (180°). The angle addition postulate states that if a point is within an angle, the measure of the angle equals the sum of the measures of the angles formed by the point and the rays. Congruent angles have the same measure.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. The Similar Solids Theorem states that if two similar solids have a scale factor of a:b, their corresponding areas will be in a ratio of a2:b2 and their corresponding volumes will be in a ratio of a3:b3. Examples of homework problems involving similar solids are provided.
12.7 notes
This document discusses similar solids and their properties. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. The Similar Solids Theorem states that if two similar solids have a scale factor of a:b, then their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. The document provides examples of homework problems involving similar solids.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.6 notes
This document contains a lesson on spheres that includes:
1) Objectives about applying the volume and surface area formulas for spheres and developing problem-solving skills
2) Examples of calculating the surface area and volume of various spheres and hemispheres
3) Word problems involving spheres that require using the volume formula
4) An assignment to complete problems #4-22 on page 842 of the homework that are even numbers.
11.3 notes
This document contains notes from a math class on the area of similar polygons. It states that if two polygons are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. It provides an example of two similar polygons where one side of polygon 1 is a/b times the corresponding side of polygon 2, and the area of polygon 1 is a^2/b^2 times the area of polygon 2. Several homework problems are assigned.
12.6 notes
This document contains a lesson on surface area and volume of spheres. It includes objectives of understanding volume formulas for spheres and applying 3D thinking skills. There are examples of calculating surface area and volume of various spheres and hemispheres with given radii or diameters. Students are assigned even problems from page 842 numbers 4 through 22 as homework.
Geometry Section 3-1 1112
This document provides definitions and examples related to parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect, and skew lines as lines in different planes that do not intersect. It also defines angles formed by parallel lines cut by a transversal, such as corresponding angles and alternate interior angles. Examples classify line segments and planes as parallel or skew, and identify angle relationships.
9.7 notes
The document discusses dilations in geometry. It defines dilations as reductions where the scale factor k is between 0 and 1, or enlargements where k is greater than 1. Dilations can be performed by multiplying the coordinates of a figure by a scalar value k. Matrices can also be used to represent dilations, with the scale factor k multiplied by the matrix of the original polygon. The document provides examples of dilation problems and assigns homework problems related to dilations.
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This document outlines the Geometry 2016 Chapter 12 unit on 3D shapes that will be covered from April 11th to April 29th. It includes the chapter sections and topics to be covered each day, such as different types of prisms and pyramids, as well as the homework assignments and assessments including quizzes, tests, and a study guide.
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3.3 notes
This document discusses six theorems for proving that two lines are parallel: (1) the corresponding angles converse theorem, (2) the alternate interior angles converse theorem, (3) the alternate exterior angles converse theorem, (4) the consecutive interior angles converse theorem, (5) using a paragraph proof, and (6) the transitive property of parallel lines theorem. It also assigns homework problems from page 165 involving using these theorems to prove lines are parallel.
5.1 5.2 notes
The document discusses midsegments and perpendicular bisectors of triangles. It states that every triangle has 3 midsegments that are parallel to the sides and half the length. It also explains that the perpendicular bisector of a segment is perpendicular at the midpoint and that any point on the bisector is equidistant from the endpoints. The perpendicular bisectors of a triangle are concurrent at the circumcenter.
3.2 notes
This document discusses parallel lines and transversals. It defines corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It states that if two parallel lines are cut by a transversal, then corresponding angles, alternate interior angles, and alternate exterior angles are congruent. It also states that if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. Students are instructed to complete guided practice problems with a partner.
5.7 notes
This document contains notes about complex numbers from a math class, including the section number, homework page and problem numbers, and date. It repeatedly lists the topic as complex numbers, and references homework problems about multiples of 5.
1.6 notes
The document is from a geometry class and discusses classifying polygons. It defines polygons as closed figures with 3 or more sides where each side intersects exactly 2 other sides. Polygons are named by listing the vertices in order. They can be convex, with no interior points, or concave, with interior points. Common polygons include triangles, quadrilaterals, pentagons, and hexagons. Regular polygons are convex, equilateral, and equiangular. Students are assigned homework problems classifying polygons.
11.5 notes
This document discusses formulas and examples for calculating the areas of circles, sectors, segments, and annuli. It introduces the formula for calculating the area of a circle as πr^2. It then provides examples of using this formula, as well as the formula for calculating the area of a sector, which is (portion of the circle) x (area of the circle). The document concludes by assigning homework problems from page 758 numbers 3 through 31 odds.
1.2 notes
This document defines key concepts about line segments and congruence. It introduces coplanar points, ways to write line segments, and the segment addition postulate which states that if point B lies between points A and C on a line, then the length of AB plus BC equals the length of AC. It also defines congruent segments as line segments with the same length and provides examples of using the segment addition postulate and defining congruent segments. The document assigns homework problems applying these concepts.
2.2 p1 notes
1) The document discusses conditional statements, which are logical statements written in an "if-then" form with a hypothesis and conclusion. Examples of conditional statements and their conversions to inverse, converse, and contrapositive forms are provided.
2) Homework problems are assigned from pages 82 and 83, involving analyzing conditional statements, determining if they are true or false, and identifying definitions as conditional statements.
3) A conditional statement can be written as a biconditional statement using "if and only if" when the conditional statement and its converse are both true. Definitions can also be written as biconditional statements.
4.1 notes
The document contains notes from a geometry lesson that discuss classifying triangles based on their sides and angles. It defines key concepts like the triangle sum theorem, which states that the sum of the interior angles of any triangle is 180 degrees. It also describes the exterior angle theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the remote interior angles. Examples are provided to illustrate these theorems.
Trig 2 notes
The document discusses the Law of Sines, which can be used to find missing parts of any triangle. It provides two cases where the Law of Sines can be used: 1) when two angles and any side are known, and 2) when two sides and the angle between them are known. It then gives examples of using the Law of Sines to find specific values like side lengths and triangle areas.
1.4 notes
This document discusses measuring and classifying angles. It defines an angle as being formed by two rays with a common endpoint called the vertex. Angles are measured in degrees using a protractor and are classified as acute (<90°), right (90°), obtuse (>90° and <180°), or straight (180°). The angle addition postulate states that if a point is within an angle, the measure of the angle equals the sum of the measures of the angles formed by the point and the rays. Congruent angles have the same measure.
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12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. The Similar Solids Theorem states that if two similar solids have a scale factor of a:b, their corresponding areas will be in a ratio of a2:b2 and their corresponding volumes will be in a ratio of a3:b3. Examples of homework problems involving similar solids are provided.
12.7 notes
This document discusses similar solids and their properties. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. The Similar Solids Theorem states that if two similar solids have a scale factor of a:b, then their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. The document provides examples of homework problems involving similar solids.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
12.6 notes
This document contains a lesson on spheres that includes:
1) Objectives about applying the volume and surface area formulas for spheres and developing problem-solving skills
2) Examples of calculating the surface area and volume of various spheres and hemispheres
3) Word problems involving spheres that require using the volume formula
4) An assignment to complete problems #4-22 on page 842 of the homework that are even numbers.
11.3 notes
This document contains notes from a math class on the area of similar polygons. It states that if two polygons are similar, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. It provides an example of two similar polygons where one side of polygon 1 is a/b times the corresponding side of polygon 2, and the area of polygon 1 is a^2/b^2 times the area of polygon 2. Several homework problems are assigned.
12.6 notes
This document contains a lesson on surface area and volume of spheres. It includes objectives of understanding volume formulas for spheres and applying 3D thinking skills. There are examples of calculating surface area and volume of various spheres and hemispheres with given radii or diameters. Students are assigned even problems from page 842 numbers 4 through 22 as homework.
Geometry Section 3-1 1112
This document provides definitions and examples related to parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect, and skew lines as lines in different planes that do not intersect. It also defines angles formed by parallel lines cut by a transversal, such as corresponding angles and alternate interior angles. Examples classify line segments and planes as parallel or skew, and identify angle relationships.
9.7 notes
The document discusses dilations in geometry. It defines dilations as reductions where the scale factor k is between 0 and 1, or enlargements where k is greater than 1. Dilations can be performed by multiplying the coordinates of a figure by a scalar value k. Matrices can also be used to represent dilations, with the scale factor k multiplied by the matrix of the original polygon. The document provides examples of dilation problems and assigns homework problems related to dilations.
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12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
12.5 notes
The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3πr^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.
12.4 notes
This document contains notes from a math lesson on finding the volumes of prisms and cylinders. It defines volume as the amount of space inside an object. It explains that to find the volume of a prism or cylinder, you calculate the area of the base and multiply it by the height. For a prism, the base can be any shape and its area formula is used. For a cylinder, the base is a circle so the volume formula is πr^2h, with r as the radius and h as the height. Examples of volume problems are shown and homework problems are assigned from the textbook.
Indian volleyball tournament
A volleyball tournament will be held on May 2nd at 9am at the Max Evans Gym to benefit the Strafford Indian Volleyball Program. The tournament will feature fun rules, games and prizes and cost $10 per person to register, either as part of a team of 6-8 players or individually. People can register their teams on Facebook or by contacting the coaches Ashley Bough or Angelina Hedrick by May 1st.
12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
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12.5 notes
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This document contains information about the law of sines for a math homework assignment. It lists the topic as the law of sines and directs the student to problems 15-17 and 29-31 on page 672 of their homework, which was assigned on April 08, 2015. The document repeats this information four times.
12.1 notes
This document contains notes from a math class where students were working on homework problems involving trigonometry (SOHCAHTOA) and multiples of 3. The notes are dated April 08, 2015 and reference homework page 648 problems 12 through 36 dealing with multiples of 3.
11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
11.6 notes
This document discusses calculating the areas of regular polygons. It defines key terms like apothem and provides two formulas for finding the area of a regular polygon: either by multiplying one half the apothem by the perimeter, or by multiplying one half the number of sides by the length of a side squared. The document includes examples of area problems involving regular polygons like nonagons and octagons.
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
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12.7 notes
- 1. 12.7 Similar Solids April 13, 2011 Bellwork 1. If the earth has a diameter of 12,756.3 km, what is the volume of the western hemisphere? 5.43 X 1011 2. If the surface area of a sphere is about 1,017.876 cm2, what is the radius of the sphere? 9 = r 3. A beach ball has a radius of 20 inches. If the white sections were removed from the beach ball, what would the remaining volume be? (assume all sections are equal in size) 22,340.2 = V HW pg. 850 #422 evens 1
- 2. 12.7 Similar Solids April 13, 2011 12.7 Similar Solids Def: 2 same type solids w/ = ratios (scale factor) HW pg. 850 #422 evens 2
- 3. 12.7 Similar Solids April 13, 2011 Similar Solids Theorem: If 2 similar solids have a scale factor of a:b, then corresponding areas have ratio of a2:b2 and corresponding volumes have ratio of a3:b3. HW pg. 850 #422 evens 3
- 4. 12.7 Similar Solids April 13, 2011 HW pg. 850 #422 evens 4
- 5. 12.7 Similar Solids April 13, 2011 12.7 HW pg. 850 #422 evens HW pg. 850 #422 evens 5