Question

The area of a quarter circle is 38.465 square inches. What is the quarter circle's radius?

Answer 1

The formula for a circle's area is $A=\pi r^2$. We are given an area of 38.465 square inches for a quarter of it.

Multiply this value by 4 to compensate for the quarter circle.

$4 \times 38.465=\pi r^2$

$153.86=\pi r^2$

Divide both sides by pi (Note: I'm using the conventional value of 3.14)

$49=r^2$

Take the positive square root of both sides

$7=r$

The radius is 7 inches. Let me know if you have any questions, thanks!