Exercise 11 Page 867

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of the corresponding linear dimensions 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 cylinders.

Let's write the ratio of the corresponding sides as a fraction and raise it to the power of three to find the scale factor of the volumes.

a/b=35/25

DivFracByFracSameDenom

.a /5./.b /5.=a/b

a/b=7/5

RaiseEqn

LHS^3=RHS^3

( a/b )^3=( 7/5 )^3

PowQuot

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

a^3/b^3 = 7^3/5^3

CalcPow

Calculate power

a^3/b^3=343/125

FracToScale

\dfrac a b = a:b

a^3:b^3=343:125

The scale factor of volumes is 343:125.