Exercise 3 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 surface areas is a^2:b^2. Consider the given cylinders.

Let's write the ratio of the radii as a fraction to find the scale factor of the surface area. Note that we want to find the ratio of the surface area of the small cylinder to the surface area of the big cylinder. Therefore, a=6, and b=15.

a/b=6/15

DivFracByFracSameDenom

.a /3./.b /3.=a/b

a/b = 2/5

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Find a^2/b^2

RaiseEqn

LHS^2=RHS^2

(a/b)^2=( 2/5 )^2

PowQuot

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

a^2/b^2 = 2^2/5^2

CalcPow

Calculate power

a^2/b^2 = 4/25

FracToScale

\dfrac a b = a:b

a^2:b^2=4:25

The scale factor of volumes is 4:25