Chapter 12.8, Problem 33STP

To determine

Find the ratio of the surface area of the large sphere to the surface area of the small sphere.

Answer to Problem 33STP

A

Explanation of Solution

Given:

Two similar spheres have radii of $20\pi$

meters and $6\pi \text{ meters}$ .

Formula Used: 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:

Ratio of the radii of the spheres is

  $\frac{20\pi }{6\pi }=\frac{10}{3}$

= 10:3

So, the ratio of the surface area of the spheres is

  ${10}^2:3^2=100:9$

So, the correct option is A.