Question

A circle has a circumference of 28π centimeters. In terms of π, what is the area of the circle to the nearest square centimeter?

Answer 1

Hi there!

The formula to find the are of a circle is :

a = $\pi$r²

The formula to find the circumference of a circle is :

c = 2$\pi$r

In order to use the area formula, you need to figure out what the radius (r) is.

If we solve for "r" in the circumference equation, we have :

r = c ÷ (2$\pi$)

Now we use this to replace "r" in the area formula :

a = $\pi$ ( c ÷ (2$\pi$))²

When we simplify this we get :

a = c² ÷ 4$\pi$

Now you can put your value of "c" into this equation and find "a".

*Remember, $\pi$ is about 3.1416.

Solving for "a" :

a = c² ÷ 4$\pi$

a = 28² ÷ 4$\pi$

28² = 28 × 28 = 784

a = 784 ÷ 4$\pi$

4$\pi$ = 4 × $\pi$ = 12.56637061435917

a = 784 ÷ 12.56637061435917

a = 62.38873769202297cm²

You need to round to the nearest square centimeter, which means that you need to round to the nearest whole number :

a = 62cm²

There you go! I really hope this helped, if there's anything just let me know! :)