Question

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.

170.1 ft2

973.1 ft2

452.3 ft2

638.5 ft2

Answer 1

`A_o=\pi r^2\\\\2r_1=26.4\ ft\to r_1=13.2\ ft;\ r_2=13.2\ ft+8.8\ ft=22\ ft\\\\Area\ of\ the\ hot\ tub:A_1=\pi\cdot13.2^2=174.24\pi\ (ft^2)\\\\Area\ of\ the\ hot\ tub+deck:A_2=\pi\cdot22^2=484\pi\ (ft^2)\\\\Area\ of\ the\ deck:A=A_2-A_1\\\\A=484\pi-174.24\pi=309.76\pi\approx309.76\cdot3.14=972.6\ (ft^2)\\\\Answer:\boxed{973.1\ ft^2}`

Answer 2

A = pie × radius ^2 Hot tub diameter = 26.4ft ÷ 2 = 13.2ft Hot tub area = pie × 13.2^2 = 174.24 × Pie(3.14) = 547.1136ft Diameter of both hot tub and deck = 26.4ft + 8.8ft + 8.8ft = 44ft A = pie (3.14) × radius^2 Radius of hot tub and deck = 22ft Area of both hot tub and deck = A = pie(3.14) × 22^2 = A = pie (3.14) × 484 = 1519.76ft Area of hot tub and deck - hot tub area = 1519.76 - 547.1136 = 972.6464ft Round it to nearest tenth = 973.1ft^2