Chapter 12, Problem 10CT

To determine

To find: The area and the volume of the sphere.

Answer to Problem 10CT

The area of the sphere is $144\pi {\text{cm}}^{\text{2}}$ and the volume of the sphere is $288\pi {\text{cm}}^{\text{3}}$ .

Explanation of Solution

Given information:

The radius of the sphere is $6\text{cm}$ .

Calculation:

Write the expression to calculate the surface area of the sphere.

  $\text{Surface}\text{area}=4\pi r^2$

Where,

• $r$ is the radius of the sphere.

Substitute the values in the above expression.

  $\begin{array}{c}\text{Surface}\text{area}=4\times \pi \times 6\times 6\\ =144\pi {\text{cm}}^{\text{2}}\end{array}$

Write the expression to calculate the volume of the sphere.

  $V=\frac{4}{3}\times \pi \times r^3$

Substitute the values in the above expression.

  $\begin{array}{c}V=\frac{4}{3}\times \pi \times 6\times 6\times 6\\ =288\pi {\text{cm}}^{\text{3}}\end{array}$

Therefore, thearea of the sphere is $144\pi {\text{cm}}^{\text{2}}$ and the volume of the sphere is $288\pi {\text{cm}}^{\text{3}}$ .