Chapter 0.2, Problem 4E

(a)

To determine

To find: The volume of a sphere as a function of the sphere’s radius $r$ .

Answer to Problem 4E

The volume of a sphere as a function of the sphere’s radius $r$ is equal to $\frac{4}{3}\pi r^3$ .

Explanation of Solution

Given information:

The radius of the sphere is $r$ .

Calculation:

The volume of a sphere is given by

  $V=\frac{4}{3}\pi r^3$ , where $r$ is a radius of the sphere.

Therefore, the volume of a sphere as a function of the sphere’s radius $r$ is $\frac{4}{3}\pi r^3$ .

(b)

To determine

To find: The volume of a sphere.

Answer to Problem 4E

The volume of a sphere is equal to $36\pi$ cube cm.

Explanation of Solution

Given information:

The radius of the sphere is $3$ cm.

Calculation:

From the part (a),

The volume of a sphere is $\frac{4}{3}\pi r^3$ , where $r$ is a radius of the sphere.

Since the radius of the sphere is $3$ cm, so the volume of the sphere is below:

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

Therefore, the volume of a sphere is $36\pi$ cube cm.