Chapter 12.7, Problem 37SPR

To determine

Calculate the volume of each sphere or hemisphere.

Answer to Problem 37SPR

The volume of the hemisphere is $1072c{m}^3$ .

Explanation of Solution

Given:

It is given in the question that the circumference of the hemisphere great circle is $50.3cm$ .

Concept Used:

In this, use the concept of volume of sphere i.e. $V=\frac{4}{3}\pi r^3$ and circumference is $C=2\pi r$ .

Calculation:

Here, $C=50.3cm$

  $\begin{array}{l}50.3cm=2\pi r\\ r=\frac{50.3}{2\pi }\\ r=\frac{50.3}{6.28}\\ r=8.00\end{array}$

Now, the volume be

  $\begin{array}{l}V=\frac{4}{3}\pi r^3\\ $ V=\frac{4}{3}\pi {(8)}^3$V=\frac{4}{3}\pi \cdot 512\\ V=\frac{6430.7}{3}\\ V=2144c{m}^3\end{array}$

Since, it is a volume of sphere and the volume of hemisphere will be $\frac{2144}{2}=1072c{m}^3$ .

Conclusion:

The volume is $1072c{m}^3$ .