Question

The circumference of a circle is 23π m. What is the area, in square meters? Express your answer in terms of \piπ

Answer 1

Area of the circle =
`(529)/(4)` π m² or 132.25 π m²

Explanation:

To find the area, we will follow the steps below.

First write down the formular for the circumference of a circle, then use the formula to find the radius of the circle after which you can now find the area of the circle.

That is;

C = 2πr

where c is the circumference of the circle and r is the radius of the circle

From the question given, circumference C = 23π

23π = 2π r

Divide both-side of the equation by 2π

23π/2π = 2πr/2π

23/2 = r

radius =
`(23)/(2)` m

Formula for calculating the area of a circle is given by;

A = πr²

where A= area of the circle and r is the radius of the circle

A = π (
`(23)/(2)` )²

A =
`(529)/(4)` π m² or 132.25 π m²

Area of the circle =
`(529)/(4)` π m² or 132.25 π m²