Chapter 12.7, Problem 38SPR

To determine

Calculate the volume of each sphere or hemisphere.

Answer to Problem 38SPR

The volume of the hemisphere is $74546.1f{t}^3$ .

Explanation of Solution

Given:

It is given in the question that the area of the hemisphere of the great circle is $3416f{t}^2$ .

Concept Used:

In this, use the concept of volume of sphere i.e. $V=\frac{4}{3}\pi r^3$ and the area for the great circle is $A=\pi r^2$ .

Calculation:

Here, $A=3416f{t}^2$

  $\begin{array}{l}3416f{t}^2=\pi r^2\\ r^2=\frac{3416}{\pi }\\ r^2=\frac{3416}{3.14}\\ r^2=1087.8\\ r=\sqrt{1087.8}\\ r=32.97ft\end{array}$

Now, the volume be

  $\begin{array}{l}V=\frac{4}{3}\pi r^3\\ $ V=\frac{4}{3}\pi {(32.9)}^3$V=\frac{4}{3}\pi \cdot 35611.2\\ V=\frac{447276.6}{3}\\ V=149092.2f{t}^3\end{array}$

Since it is a volume of sphere then the volume of the hemisphere will be $\frac{149092.2}{2}=74546.1f{t}^3$ .

Conclusion:

The volume is $74546.1f{t}^3$ .