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. 172.70 ft² 178.98 ft² 200.96 ft² 179.94 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 \(A=\pi R^{2}-\pi r^{2}\)

We know that the area of a circle is \(A=\pi r^{2}\). The area of the path is the area of the outer - circle minus the area of the inner - circle (the garden).
Substitute \(R = 11\), \(r = 8\) and \(\pi=3.14\) into the formula \(A=\pi(R^{2}-r^{2})\).
First, calculate \(R^{2}-r^{2}\):

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Then, calculate \(A\):
\(A = 3.14\times57=178.98\approx178.98\) square feet.

Answer:

\(178.98\ ft^{2}\) (corresponds to the second option \(178.98\ ft^{2}\))