Question

the circumference of a circle is 119.32 yards. what is the circles radius? round your answer to the nearest hundredth. blank yards 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 \( \pi \approx 3.14 \). 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 know that \( C = 119.32 \) yards and \( \pi\approx3.14 \). Substituting these values into the formula for \( r \), we get \( r=\frac{119.32}{2\times3.14} \).

Step3: Perform the calculation

First, calculate the denominator: \( 2\times3.14 = 6.28 \). Then, divide the numerator by the denominator: \( r=\frac{119.32}{6.28}=19.0 \) (wait, let's do the division properly: \( 119.32\div6.28 = 19.0 \)? Wait, no, let's check: \( 6.28\times19 = 119.32 \), yes. Wait, but let's do it step by step. \( 119.32\div6.28 \): divide numerator and denominator by 4: \( 29.83\div1.57 = 19.0 \). Wait, but let's use a calculator approach. \( 119.32\div(2\times3.14)=119.32\div6.28 = 19.0 \). But wait, the problem says to round to the nearest hundredth. But 19.0 is already a whole number, so as a decimal to the nearest hundredth, it's 19.00? Wait, no, wait, maybe I made a mistake. Wait, \( 2\pi r = C \), so \( r = C/(2\pi) \). Let's use \( \pi = 3.1416 \) for more accuracy. Then \( 2\pi=6.2832 \). Then \( 119.32\div6.2832\approx19.0 \) (because \( 6.2832\times19 = 119.3808 \), which is close to 119.32. Wait, maybe the given \( \pi \) is 3.14. Let's check with \( \pi = 3.14 \): \( 2\times3.14 = 6.28 \), \( 119.32\div6.28 = 19.0 \). So the radius is 19.00 yards when rounded to the nearest hundredth? Wait, no, 19 is a whole number, so in decimal form, to the nearest hundredth, it's 19.00. But let's verify: \( 2\times3.14\times19 = 119.32 \), which matches the given circumference. So the calculation is correct.

Answer:

19.00