A circle has a radius of 9 in. Find the increase in area when the radius is increased by 3 in. Round to the nearest hundredth. A) 113.10 in² B) 226.19 in² C) 452.39 in² D) 197.92 in² E) 424.12 in²

Question

Quizplus · Accepted Answer

The area of a circle is given by the formula A = πr^2. Therefore, the area of the circle with radius 9 in. is A1 = π(9^2) = 81π sq. in.
When the radius is increased by 3 in., the new radius is 12 in. Therefore, the new area is A2 = π(12^2) = 144π sq. in.
The increase in area is A2 - A1 = 144π - 81π = 63π sq. in.
To approximate this value to the nearest hundredth, we can use the approximation π ≈ 3.14. Therefore, the increase in area is approximately 63π ≈ 197.92 sq. in., which is closest to choice D.

A Circle Has a Radius of 9 In