Chapter 12.8, Problem 12PPS

To determine

Find the ratio of the volume of the large sphere to the volume of the small sphere.

Answer to Problem 12PPS

125:8

Explanation of Solution

Given:

Two spheres have surface areas of $100\pi$

square centimeters and

  $16\pi$ square centimeters .

Formula Used: If the ratio of the sides of two similar solids is a : b , then the ratio of the volume of the solids is

  $a^3:b^3$

If the ratio of the sides of two similar solids is a : b , then the ratio of the surface area of the solids is

  $a^2:b^2$

Calculation:

First , we find the scaling factor of the sides , k

Ratio of surface areas of the spheres is

  $\begin{array}{l}{k}^2=\frac{100\pi }{16\pi }=\frac{25}{4}\\ \Rightarrow k=\frac{5}{2}\end{array}$

So, the ratio of the volume of the larger sphere to the volume of the smaller sphere is $5^3:2^3=125:8$