Question

The circumference of a circle is 14 in. What is the area, in square inches?

Answer 1

15.6 in² (nearest tenth)

Explanation:

Circumference of a circle

`\large\boxed{C=2\pi r}`

Where r is the radius of the circle.

Given:

• C = 14 in

Substitute the given value into the equation for the circumference and solve for r:

`\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = (14)/(2 \pi)\\\\ r & = (7)/( \pi)\end{aligned}`

Area of a circle

`\large\boxed{A=\pi r^2}`

Where r is the radius.

Substitute the found radius into the equation for area and solve for A:

`\begin{aligned}\implies A&=\pi \left((7)/(\pi)\right)^2\\\\ A&=\pi \cdot (7^2)/(\pi^2)\\\\ A&=(49\pi)/(\pi^2)\\\\ A&=(49)/(\pi)\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}`

Therefore, the area of the circle with a circumference of 14 in is 15.6 in².