Question

1. the figure represents the overhead view of a deck surrounding a hot tub. what is the area of the deck? round to the nearest tenth. 973.1 ft² 170.1 ft² 452.3 ft² 638.5 ft²

Explanation:

Step1: Calculate the radius of the hot - tub

The diameter of the hot - tub \(d = 26.4\) ft. The radius of the hot - tub \(r_{1}=\frac{d}{2}=\frac{26.4}{2}=13.2\) ft.

Step2: Calculate the radius of the outer circle (hot - tub + deck)

The width of the deck is \(8.8\) ft. So the radius of the outer circle \(r_{2}=r_{1}+8.8=13.2 + 8.8=22\) ft.

Step3: Use the formula for the area of a circle \(A=\pi r^{2}\)

The area of the deck \(A=\pi r_{2}^{2}-\pi r_{1}^{2}=\pi(r_{2}^{2}-r_{1}^{2})\)
Substitute \(r_{1} = 13.2\) and \(r_{2}=22\) into the formula:

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Take \(\pi\approx3.14\), then \(A\approx3.14\times309.76 = 973.6464\approx973.1\) \(ft^{2}\)

Answer:

\(973.1\space ft^{2}\)