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Bingel [31]
2 years ago
6

The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. Wha

t is the area of the roof? What is the lateral area of the roof?
Mathematics
1 answer:
xz_007 [3.2K]2 years ago
5 0

Answer:

The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2

Step-by-step explanation:

The area of the roof is computed by the equation of the area of a cone:
A = πr(r + \sqrt{h^{2}+r^(2) })
(r: radius, h: height, πr^2 is the area of the base of the cone, πr\sqrt{h^{2}+r^(2) } is the lateral area of the cone). So:

A = 15\pi (15 + \sqrt{30^{2} +15^{2}  } ) ≈ 2287.44 ft^2.

As I stated earlier, the lateral area of the roof can be computed:

AL=15\pi \sqrt{30^{2} +15^{2} } ≈ 1580.58 ft^2.

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