Exercise 34 Page 898

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 areas is a^2:b^2. Consider the given solids.

Let's write the ratio of the surface areas as a fraction and take square roots to find the scale factor.

a^2/b^2=256/324

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Solve for a/b

ReduceFrac

a/b=.a /4./.b /4.

a^2/b^2=64/81

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

(a/b)^2=64/81

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a/b=sqrt(64/81)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

a/b=sqrt(64)/sqrt(81)

CalcRoot

Calculate root

a/b=8/9

FracToScale

\dfrac a b = a:b

a:b=8:9

The scale factor is 8:9. Note that we only kept the principal root when reducing the fraction because the scale factor must be a positive number. Therefore, the ratio of the height of the small prism to the height of the large prism is 8:9.