Question

the circumference of a circular painting is 56.52 feet. what is the radius of the painting? use 3.14 for π and do not round your answer.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius and \( \pi \) is given as \( 3.14 \). We know \( C = 56.52 \) feet, so we can solve for \( r \).

Step2: Substitute the known values into the formula

Substitute \( C = 56.52 \) and \( \pi = 3.14 \) into \( C = 2\pi r \):
\( 56.52 = 2\times3.14\times r \)
First, calculate \( 2\times3.14 = 6.28 \), so the equation becomes \( 56.52 = 6.28r \).

Step3: Solve for \( r \)

To find \( r \), divide both sides of the equation by \( 6.28 \):
\( r=\frac{56.52}{6.28} \)
Calculating the division, \( \frac{56.52}{6.28}=9 \).

Answer:

9