Question

The circumference of a circle is 11π inches. What is the area, in square inches, of the circle? Express your answer in terms of π. a 32.25 π b 95.03 π c 30.25 π d 17.27 π

Answer 1

`\Huge \boxed{30.25 \pi}`

Explanation:

The circumference of a circle formula is:

`C= \pi d`

The circumference is given, solve for d.

`11\pi=\pi d`

Cancel
`\pi` from both sides.

`11=d`

The radius is half the measure of the diameter.

`\displaystyle r=(11)/(2) =5.5`

The area of a circle formula is:

`A=\pi r^2`

Let r = 5.5, solve for the area.

`A=\pi (5.5)^2`

`A=\pi (30.25)=30.25\pi`

Answer 2

30.25 pi

Explanation:

The circumference of a circle is given by

C = 2 * pi *r

11 pi = 2 * pi *r

divide each side by 2 pi

11/2 = 2 ( pi) * r/ ( 2pi)

11/2 = r

We can find the area by

A = pi * r^2

= pi ( 11/2) ^2

= pi ( 121/4)

= pi ( 121/4)

= 30.25 pi