Question

question 20
1 pts
what is the radius of a circle whose circumference is 546? use = 3.1416 and round to the nearest inch.
98\
88\
88\
89\

Explanation:

Step1: Convert the circumference to inches

Since \(1\) foot \( = 12\) inches, \(54\) feet \(6\) inches \(=54\times12 + 6=648+6 = 654\) inches.

Step2: Use the formula for the circumference of a circle \(C = 2\pi r\)

We know \(C = 654\) inches and \(\pi=3.1416\). Rearranging the formula for \(r\), we get \(r=\frac{C}{2\pi}\).
Substitute \(C = 654\) and \(\pi = 3.1416\) into the formula: \(r=\frac{654}{2\times3.1416}\).
First, calculate \(2\times3.1416 = 6.2832\). Then \(r=\frac{654}{6.2832}\approx104.1\) inches. Wait, there is a mistake. Let's check the problem again. Maybe the circumference is \(546\) inches (if it's \(54\) feet \(6\) inches, \(54\times12+6 = 654\) is wrong. Wait no, \(54\) feet \(6\) inches: \(54\times12=648\), \(648 + 6=654\). But let's re - express the formula.

The formula for the circumference of a circle is \(C = 2\pi r\), so \(r=\frac{C}{2\pi}\). Given \(C = 54\times12+6=654\) inches and \(\pi = 3.1416\).

\(r=\frac{654}{2\times3.1416}=\frac{654}{6.2832}\approx104\) (wrong). Wait, no, maybe the problem was \(C = 546\) inches (a typo in the problem statement). If \(C = 546\) inches.

\(r=\frac{546}{2\times3.1416}=\frac{546}{6.2832}\approx87\) (still wrong). Wait, another approach:

The formula \(C = 2\pi r\), so \(r=\frac{C}{2\pi}\).

If \(C = 54\) feet \(6\) inches \(=54\times12 + 6=654\) inches.

\(r=\frac{654}{2\times3.1416}\approx104\) (incorrect as per options). Wait, maybe the problem is \(C = 546\) inches (a mis - write of \(54\) feet \(6\) inches as \(546\) inches).

\(r=\frac{546}{2\times3.1416}=\frac{546}{6.2832}\approx87\) (no). Wait, if \(C = 546\) (assuming \(54\) feet \(6\) inches is \(546\) inches (a wrong conversion, but let's check the options).

If we use \(C = 2\pi r\), and the options are in feet and inches. Let's convert the formula.

\(C = 2\pi r\), \(r=\frac{C}{2\pi}\).

If \(C = 54\) feet \(6\) inches \(=54.5\) feet.

\(r=\frac{54.5}{2\times3.1416}\approx8.7\) feet. Since \(1\) foot \( = 12\) inches, \(0.7\times12 = 8.4\approx8\) inches. So \(r = 8\) feet \(8\) inches.

Answer:

\(8'8''\)