Question

If the circumference of a circle is 11 pi, what is the area?

Answer 1

So our answer in pi form is 30.25π

Explanation:

The circumference of a circle is given by the formulas :

`2\pi r` or
`\pi d` where r is radius and d is the diameter

Since

11π = 2πr

We can solve for r to use it in the area of a circle formula:

`(11\pi )/(2\pi ) = r`

r = 5.5

The area of a circle is given by the formula:

`\pi r^(2)` where r is the radius/.

Since we found r we can find the area:

π(5.5)² = 30.25π

So our answer in pi form is 30.25π

Answer 2

As you have not specified the format in which to give the answer, I am giving three ways of writing it:

`\sf 30.25 \pi \ units^2`

`\sf (121)/(4) \pi \ units^2`

95.03 units² (nearest hundredth)

Explanation:

Formulae

• Circumference of a circle = 2πr
• Area of a circle = πr²

(where r is the radius)

Given:

• circumference = 11π

Therefore, use the given value and the circumference equation to find the radius:

⇒ circumference = 11π

⇒ 2πr = 11π

⇒ 2r = 11

⇒ r = 5.5

Now we have found the radius, simply substitute this into the equation for area of circle:

⇒ area of a circle = πr²

= π5.5²

= 30.25π units²