Chapter 12.4, Problem 15WE

To determine

To compare: The volume of sphere and hemisphere.

Answer to Problem 15WE

The volume of hemisphere is 4 times the volume of sphere.

Explanation of Solution

Given information:

The radius of sphere is 2 and radius of hemisphere is 4

Calculation:

The Volume of sphere is given by

  $V_1=\frac{4}{3}\pi r_1{}^3$ and

The Volume of hemisphere is given by

  $V_2=\frac{2}{3}\pi r_2{}^3$

Since, radius of sphere is $r_1=2$ . Therefore,

  $\begin{array}{l}{V}_1=\frac{4}{3}\pi {\left(2\right)}^3\\ V_1=\frac{4}{3}\pi \times 8\\ V_1=\frac{32}{3}\pi \end{array}$

Also, radius of hemisphere is $r_2=4$ . Therefore,

  $\begin{array}{l}{V}_2=\frac{2}{3}\pi {\left(4\right)}^3\\ V_2=\frac{2}{3}\pi \times 64\\ V_2=\frac{128}{3}\pi \end{array}$

Compare the volume of sphere and hemisphere. Therefore,

  $\begin{array}{l}\frac{V_2}{V_1}=\frac{\frac{128}{3}\pi }{\frac{32}{3}\pi }\\ \frac{V_2}{V_1}=\frac{4}{1}\\ V_2=4V_1\end{array}$

Hence,

The volume of hemisphere is 4 times the volume of sphere.