Chapter 12.5, Problem 22WE

To determine

To show: The ratio of the areas of two sphere is $a^2:b^2$ .

Explanation of Solution

Given information:

Two spheres have radii $a$ and $b$ .

The area of sphere is proportional to the square of radius. The ratio of the area of two spheres is,

  $\begin{array}{c}\frac{A_1}{A_2}=\frac{4\pi \times a^2}{4\pi \times b^2}\\ =\frac{a^2}{b^2}\end{array}$

From the above, it is clear that the ratio of the area of two sphere is $a^2:b^2$ .

Hence, proved.