Warm Up
• A shape has 5 faces, and 5 vertices how many edges does the shape have?
• A sphere has a radius of 7.5, what is its surface area and volume?
• What is the surface area and volume of the shape?
Exploring Similar Solids
12.7
What is similar
EXAMPLE 1 Identify similar solids
Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right.
a.b.
EXAMPLE 1 Identify similar solids
SOLUTION
The prisms are similar because the ratios of corresponding linear measures are all equal. The scale factor is 2:3.
ANSWER
The prisms are not similar because the ratios of corresponding linear measures are not all equal.
ANSWER
a. Lengths48 Widths
24 Heights
22
b. Lengths 46 Widths
23 Heights
23
12
= 12= 1
1=
23=
GUIDED PRACTICE for Example 1
Tell whether the pair of right solids is similar. Explain your reasoning.
1.
GUIDED PRACTICE for Example 1
SOLUTION
The solids are similar because the ratios of corresponding sides is in the ratio 4:3
ANSWER
43=Lengths
1612
43=Lengths
129
Ratio
• What is the pattern?• Side:• Surface Area:• Volume:
Formula
EXAMPLE 3 Find the scale factor
The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scale factor of Pyramid P to Pyramid Q.
EXAMPLE 3 Find the scale factor
SOLUTION
Use Theorem 12.13 to find the ratio of the two volumes.
a3
b3 = 1000216
The scale factor of Pyramid P to Pyramid Q is 5:3.
ANSWER
Write ratio of volumes.
Find cube roots.
Simplify.
ab = 6
10
ab = 5
3
GUIDED PRACTICE for Examples 2, 3, and 4
Cube C has a surface area of 54 square units and Cube D has a surface area of 150 square units. Find the scale factor of C to D. Find the edge length of C, and use the scale factor to find the volume of D.
3.
SOLUTION
a2
b2 = 54150 Write ratio of volumes.
Find square roots.
Simplify.
ab = 5
3
ab = 3
5
Use Theorem 12.13 to find the ratio of the two properties.
GUIDED PRACTICE for Examples 2, 3, and 4
C edgeD edge = 3
5 Use Scale Factor.
Find the edge length.
Surface area = 54 square units
Single side = 9 units
Edge length = 3 units
Find volume of D
D edge = 5
Volume of D = 125 square units
Homework
• Page 850-851– # 3- 21 odd
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