The area of a circle is pi square inches. What is the diameter?

Question

asked Dec 19, 2023 162k views

1 Answer

Zhu · Answer 1 · 2023-12-23T10:18:22+0000

We are given the area of a circle and we are asked to find its diameter. To do that, we need to remember the formula for the area of a circle:

$A=\frac{D^2\pi^{}}{4}$

Now we solve for the diameter "D". First by multiplying both sides of the equation by 4

$4A=D^2\pi$

Now we divide by pi

$(4A)/(\pi)=D^2$

Now we take square root on both sides:

$\sqrt{(4A)/(\pi)}=D$

Simplifying:

$2\sqrt[]{(A)/(\pi)}=D$

Replacing the value for the area:

$2\sqrt[]{(\pi)/(\pi)}=D$

Simplifying:

$D=2\text{inch}$