Exercise 33 Page 870

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

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

a/b = 20π/6π

ReduceFrac

a/b=.a /2π./.b /2π.

a/b = 10/3

RaiseEqn

LHS^2=RHS^2

(a/b)^2 =( 10/3 )^2

PowQuot

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

a^2/b^2 = 10^2/3^2

CalcPow

Calculate power

a^2/b^2 = 100/9

FracToScale

\dfrac a b = a:b

a^2:b^2 = 100:9

The scale factor of the areas is 100:9. Therefore, the answer is B.