Chapter 12.5, Problem 23WE

To determine

To show: The ratio of the volumeof two sphere is $a^3:b^3$ .

Explanation of Solution

Given information:

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

Volume of sphere is $\frac{4}{3}\pi r^3$ .Let’s volume of the first sphere is $V_1$ . The volume of the second sphere is $V_2$ .

The volume of sphere is proportional to the cube of radius. The ratio of the volume of two spheres is,

  $\begin{array}{c}\frac{V_1}{V_2}=\frac{\frac{4\pi }{3}\times a^3}{\frac{4\pi }{3}\times b^3}\\ =\frac{a^3}{b^3}\end{array}$

From the above, it is clear that the ratio of the volume of two sphere is $a^3:b^3$ .

Hence, proved.