Question

the exact circumference of a circle is 34π meters. what is the approximate area of the circle? use 3.14 for π. round to the nearest hundredth if necessary.

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. We know that \( C = 34\pi \) meters. So we can set up the equation \( 34\pi=2\pi r \).
To solve for \( r \), we divide both sides of the equation by \( 2\pi \):
\( r=\frac{34\pi}{2\pi}= 17 \) meters.

Step2: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). We know that \( r = 17 \) meters and \( \pi\approx3.14 \).
Substitute \( r = 17 \) and \( \pi = 3.14 \) into the formula:
\( A=3.14\times17^{2} \)

Step3: Calculate \( 17^{2} \) and then multiply by 3.14

First, calculate \( 17^{2}=17\times17 = 289 \).
Then, multiply by 3.14: \( A = 3.14\times289 \)
\( 3.14\times289=(3 + 0.14)\times289=3\times289+0.14\times289=867+40.46 = 907.46 \) square meters.

Answer:

907.46