Question

1. a circle with a radius of 2.5 in is shown. make sure that you use the correct units in your answers. (a) find the exact area of the circle. write your answer in terms of π. (b) using a calculator, approximate the area of the circle. to do the approximation, use the π button on the calculator, and round your answer to the nearest hundredth.

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Substitute the radius into the formula for part (a)

Given \(r = 2.5\) in. Substitute into \(A=\pi r^{2}\), we get \(A=\pi\times(2.5)^{2}\).
Since \((2.5)^{2}=2.5\times2.5 = 6.25\), so \(A = 6.25\pi\) square inches.

Step3: Approximate the value for part (b)

Using a calculator with the \(\pi\) button, \(A=6.25\pi\approx6.25\times3.141592654\).
\(6.25\times3.141592654 = 19.63495409\approx19.63\) square inches (rounded to the nearest hundredth).

Answer:

(a) \(6.25\pi\) square inches.
(b) \(19.63\) square inches.