Exercise 10 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 areas is a^2:b^2. Consider the given pyramids.

Let's write the scale factor as a fraction and elevate it to the power of two to find the ratio of the surface areas.

a/b=6/12

DivFracByFracSameDenom

.a /6./.b /6.=a/b

a/b = 1/2

RaiseEqn

LHS^2=RHS^2

( a/b )^2 = ( 1/2 )^2

PowQuot

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

a^2/b^2 = 1^2/2^2

CalcPow

Calculate power

a^2/b^2 = 1/4

FracToScale

\dfrac a b = a:b

a^2:b^2 = 1:4

The ratio of the surface area of the small pyramid to the surface area of the large pyramid is 1:4.