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# TechMathII - 2.6 - Area and Surface Area Day2

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### TechMathII - 2.6 - Area and Surface Area Day2

1. 1. Bell Ringer <ul><li>Find the area and Circumference: </li></ul><ul><li>Find the area of the trapezoid </li></ul>10 in. A = ½ * height * (b1 + b2) 20 25 23 30
2. 2. Objects that have length, width and depth are three-dimensional objects. Definitions:
3. 3. A three-dimensional closed object formed by Polygons is called a Polyhedron. face face base Each polygon that forms the polyhedron is called a face . The top and bottom faces are called Bases .
4. 4. Surface Area <ul><li>The Surface area (SA) of a three-dimensional figure is the sum of the areas of each face of the figure. </li></ul>
5. 5. 11 in 6 in 8 in If you wanted to gift-wrap this box you would need to find the surface area: SA= Area of Area of two Area of two two bases + 6*11 faces + 8*11 faces 2 (8*6) + 2 (6*11) + 2(8*11) 2 ( 48) + 2 (66) + 2 (88) 96 + 132 176 404 in square SURFACE AREA
6. 6. Find the Surface area of the following: 6ft 7ft 12 ft 3in 3in 6in 11 in L=24 in W=18in h = 7in You try!
7. 7. A Prism is a polyhedron that has two parallel polygons bases and the other faces are parallelograms.
8. 9. Volume of a rectangular box If the rectangular box were filled with 1 cm cubes, there would be 6 x 2 cubes in the bottom layer and there are 3 layers. V = (Area of Base) * h So: Volume = (L * W) * h = (6 * 2) * 3 = 12 * 3 = 36 cm³
9. 10. IF you wanted to fill this box with packing peanuts, you would need to know the volume of the box. To find this you find the area of the base then multiply It by the height of the box. 11 in 8 in 6 in (8 * 6) 11 (48) 11 528 cubic inces VOLUME
10. 11. You try! <ul><li>Find the Volume of: </li></ul><ul><li>Water it will take to fill a rectangular fish tank: 50 inches in length, 20 inches in width that you will fill to 8 inches in depth. </li></ul><ul><li>Air enclosed in a speaker box that is 52 inches high, 23 inches wide and 18 inches deep. </li></ul>
11. 12. Cylinders <ul><li>A cylinder is a three-dimensional figure that consists of two parallel, congruent circular bases and a lateral surface that connects the boundaries of the bases. </li></ul><ul><li>http://www.teachertube.com/members/viewVideo.php?video_id=10174&title=Mr_Blue__s_Total_Surface_Area </li></ul>
12. 14. TO FIND THE SURFACE AREA OF A CYLINDER: You have two congruent circles and one rectangle (the length of the rectangle is the circumference of the circle) SA= 2πr² + 2πrh Area of 2 circles + Circumference times height
13. 15. EXAMPLE This soup can has a diameter of 2.625 inches and a height of 3.875 inches. To find the Surface area and volume the soup can: First find the radius of the can 2.625 = 1.3125 2 Next use the Next use the Surface area formula: SA= 2πr² + 2πrh SA= (2 * 3.14 * 1.3125²) + (2 * 3.14 * 1.3125 * 3.875) SA = 10.82 + 31.94 SA = 42.76 Next use the formula to fine the Volume: (area of the base times height) V = Bh = πr²h V = 3.14 * 1.3125² * 3.875 V = 20.96
14. 16. You Try: Find the area and volume Diameter is 22 meters Height is 53 meters SA= 2πr² + 2πrh V = Bh = πr²h
15. 17. Surface Area and Volume of a Sphere <ul><li>Example : </li></ul><ul><li>SA = 4πr² V = 4/3 πr³ </li></ul><ul><li>SA=(4)(3.14)(3²) V = 4/3 * 3.14 * 3³ </li></ul><ul><li>SA=(4) (3.14)(9) V = 4/3 * 3.14 * 27 </li></ul><ul><li>SA = 113.04 ft² V = 113.04 cubic feet </li></ul>The radius of the Weather balloon is 3 feet
16. 18. You Try! <ul><li>Find the Surface Area and Volume of a Basketball with a radius of 50 cm. </li></ul><ul><li>SA = 4πr² V = 4/3 πr³ </li></ul>
17. 19. Surface Area and Volume of a Prism SA = the sum of the area of the base and the faces V = Bh (where B is the area of the base and h is the height)