Chapter 12, Problem 15CR

To determine

To find: The volume of a sphere with area $484\text{π}{\text{cm}}^2$ .

Answer to Problem 15CR

The volume of the sphere is $\frac{5324\text{π}}{3}{\text{cm}}^3$ .

Explanation of Solution

Given information: Area of a sphere is $484\text{π}{\text{cm}}^2$ .

Calculation:

To find the volume, first find the radius of sphere.

The formula for area of a sphere is:

  $A=4\text{π}{r}^2$

Substitute $484\text{π}$ for $A$ in the formula.

  $\begin{array}{c}484\text{π}=4\text{π}{r}^2\\ \frac{484\text{π}}{4\text{π}}=r^2\\ \sqrt{121}=r\\ 11=r\end{array}$

So, the radius of the sphere is $11\text{cm}$ .

The formula for the volume of a sphere is:

  $V=\frac{4}{3}\text{π}{r}^3$

Substitute 11 for $r$ in the formula.

  $\begin{array}{c}V=\frac{4}{3}\text{π}\cdot {\left(11\right)}^3\\ =\frac{4}{3}\text{π}\cdot 1331\\ =\frac{5324\text{π}}{3}\end{array}$

Therefore, the volume of the sphereis $\frac{5324\text{π}}{3}{\text{cm}}^3$ .