Question

the circumference of a circle is 213.52 inches. what is the circles radius? round your answer to the nearest hundredth. inches submit

Explanation:

Step1: Recall circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. We know \( C = 213.52 \) inches and we need to solve for \( r \).

Step2: Solve for \( r \)

First, we can rearrange the formula to \( r=\frac{C}{2\pi} \). Substituting \( C = 213.52 \) and using \( \pi\approx3.14 \), we get \( r=\frac{213.52}{2\times3.14} \).

Step3: Calculate the denominator

Calculate \( 2\times3.14 = 6.28 \).

Step4: Divide to find \( r \)

Now, divide \( 213.52 \) by \( 6.28 \): \( \frac{213.52}{6.28}=34.0 \). Wait, let's check the calculation again. Wait, \( 213.52\div6.28 \): \( 6.28\times34 = 6.28\times30+6.28\times4 = 188.4 + 25.12 = 213.52 \). So \( r = 34.00 \) when rounded to the nearest hundredth? Wait, no, wait, maybe I made a mistake. Wait, the formula is \( C = 2\pi r \), so \( r=\frac{C}{2\pi} \). Let's use a more accurate \( \pi \), like \( \pi = 3.1416 \). Then \( 2\pi=6.2832 \). Then \( 213.52\div6.2832\approx34.0 \). Wait, but let's do the division properly. \( 213.52\div(2\times3.14)=213.52\div6.28 \). Let's divide 213.52 by 6.28: 6.28 times 34 is 213.52, so yes, \( r = 34.00 \) inches when rounded to the nearest hundredth. Wait, but maybe the problem expects using \( \pi = 3.14 \), so the calculation is correct. Wait, but let's check again. Wait, 2 times pi times r equals circumference. So if r is 34, then 23.1434 = 213.52, which matches the given circumference. So the radius is 34.00 inches? Wait, but maybe I miscalculated. Wait, 23.14 is 6.28. 6.2834: 634=204, 0.2834=9.52, so 204+9.52=213.52. Yes, so that's correct. So the radius is 34.00 inches. Wait, but the problem says "round to the nearest hundredth". 34.00 is already to the nearest hundredth. Wait, but maybe the initial calculation was wrong? Wait, no, let's see: 213.52 divided by (2*3.14) is 213.52/6.28=34. So the radius is 34.00 inches.

Answer:

34.00