Chapter 12.7, Problem 35SPR

To determine

Calculate the volume of each sphere or hemisphere.

Answer to Problem 35SPR

The volume of the sphere is $735.1m^3$ .

Explanation of Solution

Given:

It is given in the question that the area of the great circle is $98.5m^2$ .

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, $A=98.5m^2$

  $\begin{array}{l}98.5m^2=\pi r^2\\ r^2=\frac{98.5}{3.14}\\ r^2=31.36\\ r=\sqrt{31.36}\\ r=5.6\end{array}$

Now, the volume be

  $\begin{array}{l}V=\frac{4}{3}\pi r^3\\ $ V=\frac{4}{3}\pi {(5.6)}^3$V=\frac{4}{3}\pi \cdot 175.6\\ V=735.1m^3\end{array}$

Conclusion:

The volume is $735.1m^3$ .