Chapter 1, Problem 12STP

(a)

To determine

To write: The expression for the volume of a sphere with radius $r$ .

Answer to Problem 12STP

The expression for the volume of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$ .

Explanation of Solution

Given information:

The given sphere is as follows.

  

Calculation:

Write the expression for the volume of a sphere with radius $r$ .

  $V=\frac{4}{3}\pi r^3$

Where,

• $V$ is the volume.
• $r$ is radius of the sphere.

(b)

To determine

To find: The volume of a sphere with radius of $6\text{cm}$ .

Answer to Problem 12STP

Thevolume of the sphere is $288\pi$ .

Explanation of Solution

Given information:

The radius is $6\text{cm}$ .

Calculation:

Write the expression for the volume of a sphere with radius $r$ .

  $V=\frac{4}{3}\pi r^3$

Where,

• $V$ is the volume.
• $r$ is radius of the sphere.

Substitute $6$ for $r$ in the above formula to calculate the volume of sphere,

  $\begin{array}{c}V=\frac{4}{3}\pi {\left(6\right)}^3\\ =\frac{4}{3}\pi \times 216\\ =288\pi \end{array}$

Therefore, the volume of the sphere is $288\pi$ .