Question

find the circumference and area of the circle. express answers in terms of π and then round to the nearest tenth

find the circumference in terms of π
c = □ (type an exact answer in terms of π.)
find the circumference rounded to the nearest tenth.
c = □
find the area in terms of π
a = □ (type an exact answer in terms of π)
find the area rounded to the nearest tenth
a = □

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 \(r = 4\) cm.
\(C=2\pi\times4 = 8\pi\)

Step2: Calculate the numerical value of the circumference

Using \(\pi\approx3.14\), \(C = 8\times3.14=25.12\approx25.1\)

Step3: Recall the formula for area

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 4\) cm.
\(A=\pi\times4^{2}=\pi\times16 = 16\pi\)

Step4: Calculate the numerical value of the area

Using \(\pi\approx3.14\), \(A=16\times3.14 = 50.24\approx50.2\)

Answer:

Find the circumference in terms of \(\pi\): \(C = 8\pi\)
Find the circumference rounded to the nearest tenth: \(C\approx25.1\)
Find the area in terms of \(\pi\): \(A = 16\pi\)
Find the area rounded to the nearest tenth: \(A\approx50.2\)