Chapter 12.5, Problem 1ST2

To determine

Tofind:The area and volume of sphere with diameter $6\text{cm}$ .

Answer to Problem 1ST2

The area and volume of sphere with diameter $6\text{cm}$ are equal to $36\pi {\text{cm}}^2$ and $36\pi {\text{cm}}^3$ respectively.

Explanation of Solution

Given information:The diameter of the sphere is $6\text{cm}$ .

Calculation:

The radius of sphere is always the half of the diameter of sphere.So, the radius of sphere is:

  $\begin{array}{c}\text{radius}=\frac{6}{2}\text{cm}\\ =3\text{cm}\end{array}$

The formula for the area of sphere is $4\pi r^2$ .

Substitute $3$ for $r$ in the formula for area.

  $\begin{array}{c}\text{Area}=4\pi r^2\\ =4\pi {\left(3\text{cm}\right)}^2\\ =4\pi \times 9{\text{cm}}^2\\ =36\pi {\text{cm}}^2\end{array}$

So, the area of the sphere is equal to $36\pi {\text{cm}}^2$ .

The formula for the volume of sphere $\frac{4}{3}\pi r^3$ .

Substitute $3$ for $r$ in the formula for volume.

  $\begin{array}{c}\text{V}=\frac{4}{3}\pi r^3\\ =\frac{4}{3}\pi {\left(3\text{cm}\right)}^3\\ =\frac{4}{3}\pi \times 27{\text{cm}}^3\\ =36\pi {\text{cm}}^3\end{array}$

So, the volume of the sphere is equal to $36\pi {\text{cm}}^3$ .

Therefore, the area and volume of sphere with diameter $6\text{cm}$ are equal to $36\pi {\text{cm}}^2$ and $36\pi {\text{cm}}^3$ respectively.