Question

the diameter of a circle is 10 mm.
answer the parts below. make sure that you use the correct units in your answers.
if necessary, refer to the list of geometry formulas.
(a) find the exact circumference and area of the circle. write your answers in
terms of π.
exact circumference: exact area:
(b) approximate the circumference and area of the circle. to do the
approximations, use the π button on the aleks calculator and round your
answers to the nearest hundredth.
approximate circumference: approximate area:

Explanation:

Step1: Find the radius

Since the diameter \(d = 10\) mm, the radius \(r=\frac{d}{2}=\frac{10}{2}=5\) mm.

Step2: Calculate the exact circumference

The formula for the circumference of a circle is \(C = 2\pi r\) or \(C=\pi d\). Using \(C=\pi d\), with \(d = 10\) mm, we get \(C = 10\pi\) mm.

Step3: Calculate the exact area

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 5\) mm, we have \(A=\pi\times(5)^{2}=25\pi\) \(mm^{2}\).

Step4: Calculate the approximate circumference

Using \(\pi\approx3.14159\) and \(C = 10\pi\), then \(C\approx10\times3.14159 = 31.42\) mm (rounded to the nearest hundredth).

Step5: Calculate the approximate area

Using \(\pi\approx3.14159\) and \(A = 25\pi\), then \(A\approx25\times3.14159=78.54\) \(mm^{2}\) (rounded to the nearest hundredth).

Answer:

(a) Exact circumference: \(10\pi\) mm; Exact area: \(25\pi\) \(mm^{2}\)
(b) Approximate circumference: \(31.42\) mm; Approximate area: \(78.54\) \(mm^{2}\)