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! :)