Chapter 12.4, Problem 11WE

To determine

To find: The diameter of the sphere.

Answer to Problem 11WE

Diameter of the sphere is 1 cm.

Explanation of Solution

Given information:

The area of the sphere is $\pi {\text{ cm}}^2$ .

Calculation:

The Area of sphere is given by

  $A=4\pi r^2$ and

The diameter of the sphere is doubled of its radius. So,

Diameter $D=2r$ .

Here, area $A=\pi {\text{ cm}}^2$ . Therefore,

  $\begin{array}{l}4\pi r^2=\pi {\text{ cm}}^2\\ r^2=\frac{\pi }{4\pi }{\text{ cm}}^2\\ r=\sqrt{\frac{1}{4}}\text{ cm}\\ r=\frac{1}{2}\text{ cm}\end{array}$

Thus, diameter is

  $\begin{array}{l}D=2\times \frac{1}{2}\text{ cm}\\ D=1\text{ cm}\end{array}$

Hence,

Diameter of the sphere is 1 cm.