Exercise 33 Page 754

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. Consider the given solids.

Let's write the ratio of the corresponding sides as a fraction to find the scale factor of the volumes.

a/b=3/4

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Find a^3/b^3

RaiseEqn

LHS^3=RHS^3

(a/b)^3=( 3/4 )^3

PowQuot

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

a^3/b^3 = 3^3/4^3

CalcPow

Calculate power

a^3/b^3 = 27/64

FracToScale

\dfrac a b = a:b

a^3:b^3=27:64

The scale factor of volumes is 27:64.