Question

a circle with a radius of 3 mm is shown. make sure that you use the correct units in your answers. (a) find the circumference of the circle. write your answer in terms of π. (b) using a calculator, approximate the circumference 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 circumference

The formula for the circumference of a circle is \(C = 2\pi r\) (where \(r\) is the radius). Given \(r = 25\) mm.

Step2: Calculate the circumference in terms of \(\pi\)

Substitute \(r = 25\) into \(C = 2\pi r\). So \(C=2\pi\times25 = 50\pi\) mm.

Step3: Approximate using \(\pi\approx3.14\)

Substitute \(\pi = 3.14\) into \(C = 50\pi\). Then \(C=50\times3.14=157\) mm.

Answer:

(a) \(50\pi\) mm
(b) \(157\) mm