This document provides examples and explanations for finding the surface areas and volumes of similar solids using scale factors. It begins with examples calculating surface areas and volumes when given a scale factor. It then explains that for similar solids, the surface area ratio is equal to the square of the scale factor ratio, and the volume ratio is equal to the cube of the scale factor ratio. Several multi-step word problems demonstrate applying these rules.
for GCSE students great for revision and class work as there is GCSE style questions on this wonderful power point also students can evaluate their work against the GCSE specification if you find that this is too hard for students to understand please leave a comment and i will make adjustments to the power point and make it more simple so the student will understand what to do when learning about volume and surface area of shapes.
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Sectors of the Indian Economy - Class 10 Study Notes pdf
(8) Lesson 8.6
1. Course 3, Lesson 8-6
Find the lateral and total surface areas of each solid. Round to the
nearest tenth if necessary.
1. 2.
3. What is the approximate surface area of the cone shown below?
7. Course 3, Lesson 8-6
Geometry
Words If Solid X is similar to Solid Y by a scale factor, then the
surface area of X is equal to the surface area of Y times the
square of the scale factor.
8. 1
Need Another Example?
2
3
Step-by-Step Example
1. The surface area of a rectangular prism is 78 square centimeters.
What is the surface area of a similar prism that is 3 times as large?
S.A. = 78 × 32 Multiply by the square of the scale factor.
S.A. = 78 × 9 Square 3.
S.A. = 702 cm2 Simplify
9. Answer
Need Another Example?
The surface area of a rectangular prism is 90 square
inches. What is the surface area of a similar prism that
is larger by a scale factor of 5?
2,250 in2
10. Course 3, Lesson 8-6
Geometry
Words If Solid X is similar to Solid Y by a scale factor, then the
volume of X is equal to the volume of Y times the cube of the
scale factor.
11. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. A triangular prism has a volume of 432 cubic yards. If
the prism is reduced to one third its original size, what
is the volume of the new prism?
V = 432 × Multiply by the cube of the scale factor.
V = 432 ×
V = 16 yd3 Simplify
The volume of the new prism is 16 cubic yards.
Cube .
12. Answer
Need Another Example?
A triangular prism has a volume of 96 cubic feet.
If the prism is reduced to one half its original
dimensions, what is the volume of the new prism?
12 ft3
13. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. The measurements for a standard hockey puck are
shown at the right. A giant hockey puck is 40 times
the size of a standard puck. Find the volume and
surface area of the giant puck. Use 3.14 for π.
Find the volume and surface area of the standard puck first.
V = πr2h
Find the volume and surface area of the giant puck using the computations
for the standard puck and the scale factor.
V = V(40)3
S.A. = S.A.(40)2
The giant hockey puck has a volume of about 452,160 cubic inches
and a surface area of about 37,680 square inches.
= (7.065)(40)3
= 452,160 in3
≈ (3.14)(1.5)2(1)
≈ 7.065 in3
= (23.55)(40)2
= 37,680 in2
S.A. = 2(πr2) + 2πrh
≈ 14.13 + 9.42
≈ 23.55 in2
≈ 2(3.14)(1.5)2 + 2(3.14)(1.5)(1)
14. Answer
Need Another Example?
A standard can of soup has the dimensions shown below. The radius
and height of a large can of soup are about 2 times the radius and
height of a standard-sized can. Find the surface area and volume of
the large can. Use 3.14 for π. Round to the nearest tenth.
1,081.7 cm2 ; 2,653.3 cm3
15. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-6
Geometry
16. How did what you learned
today help you answer the
WHY are formulas important
in math and science?
Course 3, Lesson 8-6
Geometry
Sample answers:
• Surface Area of Similar Solids - If solid X is similar to
solid Y by a scale factor, then the surface area of X is
equal to the surface area of Y times the square of the
scale factor.
• Volume of Similar Solids - If Solid X is similar to Solid Y
by a scale factor, then the volume of X is equal to the
volume of Y times the cube of the scale factor.
17. How is the scale factor
between two similar solids
related to the ratio of the
surface area of the solids
and to the ratio of the
volumes of the solids?
Course 3, Lesson 8-6
Ratios and Proportional RelationshipsFunctionsGeometry
