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.
An image of a circle with diameter 5.4 m inside of a larger circle. The distance from the small circle to the larger circle is 2.2m.
(1 point)
Responses
75.4 m²
75.4 m²
52.5 m²
52.5 m²
278.7 m²
278.7 m²
22.9 m²
22.9 m²
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To find the area of the deck, we need to find the difference in the areas of the larger circle and the smaller circle.
The radius of the smaller circle is half of its diameter, so the radius is 5.4 m / 2 = 2.7 m.
The radius of the larger circle is the sum of the radius of the smaller circle and the distance between the two circles, so the radius is 2.7 m + 2.2 m = 4.9 m.
The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius.
The area of the smaller circle is π(2.7 m)^2 = 22.9 m².
The area of the larger circle is π(4.9 m)^2 = 75.4 m².
Therefore, the area of the deck is 75.4 m² - 22.9 m² = 52.5 m².
The correct answer is 52.5 m².