Exercise 96 Page 636

a We know that the solids are similar. Also we know that in a prism the base areas are congruent shapes. With this information we can identify corresponding sides in our solids.

We want to determine the ratio of corresponding sides of Solid B to Solid A. This means we should divide a side in Solid B with its corresponding side in Solid A. From Part A, we identified that the 8 units side in Solid B corresponds to the side in Solid A that is 6 units. 8/6 ⇔ 4/3

b To find the area of a shape given the area of a similar shape, we should multiply the given area by the area scale factor between the shapes. This is equal to the square of the linear scale factor.

Area scale factor=(Linear scale factor)^2From Part B, we know that the linear scale factor between the solids is 43. With this information we can determine the area scale factor.

Area scale factor=(Linear scale factor)^2

Substitute

Linear scale factor= 4/3

Area scale factor=( 4/3)^2

PowQuot

(a/b)^m=a^m/b^m

Area scale factor=16/9

Now we can find the base area of Solid B by multiplying the base area of Solid A by the area scale factor. 27(16/9)=48 The base area of Solid B is 48 square units.

c To find the volume of a shape given the area of a similar shape, we should multiply the given area by the volume scale factor between the shapes. This is equal to the cube of the linear scale factor.

Volume scale factor=(Linear scale factor)^3From Part B, we know that the linear scale factor between the solids is 43. With this information we can determine the volume scale factor.

Volume scale factor=(Linear scale factor)^3

Substitute

Linear scale factor= 4/3

Volume scale factor=( 4/3)^3

PowQuot

(a/b)^m=a^m/b^m

Volume scale factor=64/27

Now we can find the volume of Solid B by multiplying the volume of Solid A by the volume scale factor. 135(64/27)=320 The volume of Solid B is 320 cubic units.

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Exercise 96 Page 636

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