Exercise 4 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 spheres.

Let's write the ratio of the volumes as a fraction and take cube roots to find the scale factor. Note that we want to find the ratio of the radius of the small sphere to the radius of the big sphere.

a^3/b^3=36/288

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Solve for a/b

ReduceFrac

a/b=.a /36./.b /36.

a^3/b^3=1/8

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

(a/b)^3=1/8

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a/b=sqrt(1/8)

SqrtQuot

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

a/b=sqrt(1)/sqrt(8)

CalcRoot

Calculate root

a/b=1/2

FracToScale

\dfrac a b = a:b

a:b=1:2

The scale factor is 1:2.