Question

the circumference of a circle is 106.76 millimeters. what is the circles radius? round your answer to the nearest hundredth. millimeters submit

Explanation:

Step1: Recall the formula for the circumference of a circle.

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius and \( \pi \) is approximately \( 3.14 \). We need to solve for \( r \), so we can rearrange the formula to \( r=\frac{C}{2\pi} \).

Step2: Substitute the given circumference into the formula.

We are given that \( C = 106.76 \) millimeters. Substituting this into the formula for \( r \), we get \( r=\frac{106.76}{2\times3.14} \).

Step3: Perform the calculation.

First, calculate the denominator: \( 2\times3.14 = 6.28 \). Then, divide the numerator by the denominator: \( r=\frac{106.76}{6.28}=17.0 \). Wait, let's check that division again. \( 106.76\div6.28 \): \( 6.28\times17 = 106.76 \), so \( r = 17.00 \) when rounded to the nearest hundredth? Wait, no, wait, maybe I made a mistake. Wait, \( 2\pi r = C \), so \( r=\frac{C}{2\pi} \). Let's use a more accurate value of \( \pi \), say \( \pi\approx3.1416 \). Then \( 2\pi\approx6.2832 \). Then \( r = \frac{106.76}{6.2832}\approx17.0 \) (since \( 6.2832\times17 = 106.8144 \), which is close to 106.76. Wait, maybe the original calculation with \( \pi = 3.14 \) is correct. Let's do \( 106.76\div(2\times3.14)=106.76\div6.28 = 17 \). So the radius is 17.00 millimeters when rounded to the nearest hundredth? Wait, 17 is already a whole number, so to the nearest hundredth, it's 17.00? Wait, no, maybe I messed up. Wait, let's recalculate: \( 2\times3.14 = 6.28 \). \( 6.28\times17 = 106.76 \), exactly. So \( r = 17.00 \) when rounded to the nearest hundredth? Wait, 17 is an integer, so to the nearest hundredth, it's 17.00. But maybe the problem expects using \( \pi = 3.14 \), so the calculation is \( 106.76\div(2\times3.14)=106.76\div6.28 = 17 \). So the radius is 17.00 millimeters? Wait, no, 17 is a whole number, so when rounded to the nearest hundredth, it's 17.00. But let's check again. The circumference formula is \( C = 2\pi r \), so solving for \( r \), we have \( r=\frac{C}{2\pi} \). Plugging in \( C = 106.76 \) and \( \pi\approx3.14 \), we get \( r=\frac{106.76}{2\times3.14}=\frac{106.76}{6.28}=17 \). So the radius is 17.00 millimeters when rounded to the nearest hundredth.

Answer:

17.00