Question

question 8 (5 points)
listen
what is the area of a circle that has a circumference of 42 inches?
a) 21.04 in²
b) 140.4 in²
c) 132.62 in²
d) 126.60 in²

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C = 42\) inches, we can solve for \(r\):

$$r=\frac{C}{2\pi}=\frac{42}{2\pi}=\frac{21}{\pi}$$

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = \frac{21}{\pi}\) into the formula:

$$A=\pi\times(\frac{21}{\pi})^{2}=\pi\times\frac{441}{\pi^{2}}=\frac{441}{\pi}$$

Using \(\pi\approx3.14\), we get \(A=\frac{441}{3.14}\approx140.4\)

Answer:

B. \(140.4\ in^{2}\)