Chapter 12.4, Problem 56SPR

To determine

Find the diameter of the circle.

Answer to Problem 56SPR

The diameter of the circle is 8.4 meters.

Explanation of Solution

Given:

The area of a circle is 54 square meters.

Formula Used:

Area of a circle with radius r :

  $A=\pi r$

Calculation:

Given A = 54 square meters

Also,

  $\begin{array}{l}A=\pi r\\ \Rightarrow \pi r=54\\ \Rightarrow r^2=\frac{54}{\pi }\mathrm{...........}[divide\text{ each side by }\pi \text{]}\\ \Rightarrow r=\sqrt{\frac{54}{\pi }}\mathrm{..........}[\text{take square root each side]}\\ \Rightarrow r\approx 4.2m\\ \Rightarrow diameter=2r\approx 8.4m\end{array}$

Hence ,

The diameter of the circle is 8.4 meters.