Exercise 5 Page 819

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of the corresponding linear dimensions of the similar solids is the scale factor. If the scale factor of two similar solids is a:b, then the ratio of their corresponding volumes is a^3:b^3. Let's illustrate the described solids.

Let's write the ratio of the corresponding sides as a fraction and to find the scale factor of the volumes. In this case, we know that each dimension of the smaller prism is scaled by a factor of 2. Therefore, if we call one of the original sides x, the length of the corresponding one would be 2x.

a/b=2x/x

ReduceFrac

a/b=.a /x./.b /x.

a/b=2/1

The scale factor is 2:1. We can now cube each number to obtain the scale factor of the volumes of the figures.

a/b=2/1

RaiseEqn

LHS^3=RHS^3

(a/b)^3=(2/1)^2

PowQuot

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

a^3/b^3=8/1

FracToScale

\dfrac a b = a:b

a^3:b^3=8:1

The ratio of the volumes is 8:1. We know that the volume of the smaller figure is 204inches^3. If we let y be the volume of the larger figure, the ratio of y to 204 is 8:1.

y/204=8/1

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Solve for y

DivByOne

a/1=a

y/204=8

MultEqn

LHS * 204=RHS* 204

y=204 * 8

Multiply

Multiply

y=1632

The volume of the larger figure is 1632inches^3, which corresponds to option D.