Question

the fence around a circular garden is 18 feet long. what is the area of the garden to the nearest square foot? use 3.14 for π. type the answer in the box. square feet

Explanation:

Step1: Find the radius from the circumference

The circumference \( C \) of a circle is given by \( C = 2\pi r \). We know \( C = 18 \) feet and \( \pi = 3.14 \). So we solve for \( r \):
\( 18 = 2 \times 3.14 \times r \)
\( 18 = 6.28r \)
\( r=\frac{18}{6.28}\approx2.87 \) feet.

Step2: Calculate the area of the circle

The area \( A \) of a circle is given by \( A=\pi r^{2} \). Substitute \( r\approx2.87 \) and \( \pi = 3.14 \):
\( A = 3.14\times(2.87)^{2}\)
First, calculate \( (2.87)^{2}\approx8.2369 \)
Then, \( A = 3.14\times8.2369\approx25.86 \)
Rounding to the nearest square foot, \( A\approx26 \).

Answer:

26