Question

The circumference of a circle is 137 in. What is the area, in square inches?

Express your answer in terms of pi.

Answer 1

`A= (18769)/(4 \pi)`

Explanation:

The formula for the circumference of a circle is
`C=2\pi r`, where C is the circumference and r is the radius. The formula for the area of a circle is
`A=\pi r^2`, where A is the area and r is the radius. To find the area, we need to find the radius.

Since we know the circumference but not the radius, we set up the circumference formula with r as the unknown:
`137=2\pi x`. We divide
`2 \pi\\` into both sides to get the radius:
`x=(137)/(2 \pi)`. (We leave pi, as it is asking in terms of pi).

Now, we plug the radius into the formula for area:
`A= \pi ((137)/(2 \pi))^2`. First, we double the radius:
`A= \pi (18769)/(4 \pi ^2)` and then we simplify the right side of the equation again by multiplying:
`A= (18769 \pi )/(4 \pi ^2)`. Then, we cancel out pi on both sides to finally get the area:
`A= (18769)/(4 \pi)`.