Chapter 12.4, Problem 57SPR

To determine

Find the diameter of the circle.

Answer to Problem 57SPR

The diameter of the circle is 11.4 cm.

Explanation of Solution

Given:

The area of a circle is 102 square centimeters.

Formula Used:

Area of a circle with radius r :

  $A=\pi r$

Calculation:

Given A = 102 square centimeters

Also,

  $\begin{array}{l}A=\pi r\\ \Rightarrow \pi r=102\\ \Rightarrow r^2=\frac{102}{\pi }\mathrm{...........}[divide\text{ each side by }\pi \text{]}\\ \Rightarrow r=\sqrt{\frac{102}{\pi }}\mathrm{..........}[\text{take square root each side]}\\ \Rightarrow diameter=2r=2\sqrt{\frac{102}{\pi }}\approx 11.4cm\end{array}$

Hence ,

The diameter of the circle is 11.4 cm.