Question

a circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. what is the approximate area of the path alone? use 3.14 for π. 178.98 ft² 172.70 ft² 379.94 ft² 200.96 ft²

Explanation:

Step1: Calculate the radius of the outer circle

The radius of the garden \(r = 8\) feet, and the width of the path is \(3\) feet. So the radius of the outer circle \(R=r + 3=8 + 3=11\) feet.

Step2: Use the formula for the area of a circle \(A=\pi R^{2}-\pi r^{2}=\pi(R^{2}-r^{2})\)

Substitute \(R = 11\), \(r = 8\), and \(\pi=3.14\) into the formula.
First, calculate \(R^{2}-r^{2}\):
\(R^{2}-r^{2}=11^{2}-8^{2}=(11 + 8)(11 - 8)\) (using the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\))
\(=(19)\times(3)=57\)
Then, calculate \(A=\pi(R^{2}-r^{2})\)
\(A = 3.14\times57\)
\(A=178.98\) square feet

Answer:

\(178.98\mathrm{ft}^{2}\)