Question

find the diameter of each circle. use your calculators value of π. round your answer to the nearest tenth. 21) area = 201.1 in² 16 in 22) area = 78.5 ft² 10 ft

Explanation:

Step1: Recall area - diameter formula

The area formula of a circle is $A=\pi r^{2}$, and $d = 2r$ (where $A$ is the area, $r$ is the radius and $d$ is the diameter). So $A=\pi(\frac{d}{2})^{2}=\frac{\pi d^{2}}{4}$, and we can solve for $d$: $d = 2\sqrt{\frac{A}{\pi}}$.

Step2: Solve for diameter in 21)

Given $A = 201.1$ in², substituting into $d = 2\sqrt{\frac{A}{\pi}}$, we have $d=2\sqrt{\frac{201.1}{\pi}}$. Using a calculator, $d = 2\sqrt{\frac{201.1}{3.14159}}\approx2\sqrt{64.012}\approx 2\times8.001\approx16.0$ in.

Step3: Solve for diameter in 22)

Given $A = 78.5$ ft², substituting into $d = 2\sqrt{\frac{A}{\pi}}$, we get $d=2\sqrt{\frac{78.5}{\pi}}$. Using a calculator, $d = 2\sqrt{\frac{78.5}{3.14159}}\approx2\sqrt{24.987}\approx 2\times4.999\approx10.0$ ft.

Answer:

1. 16.0 in
2. 10.0 ft