The roof of the 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. What is the area of the roof? Round your answer to the nearest tenth.

Answer 1

The area of the roof, A, is given by

A = πrL

where r = the radius of the base and

L = the slant height, the distance from the apex of the cone to the perimeter of its circular base.

Since L = √(r² + h²), where h = height,

the area can be written as a function of r and h

A = πr√(r² + h²)

Plugging in h = 30 and r = 15

A = π(15)√((15)² + (30)²) = 15π√(1125) ≈ 503.11π ≈ 1580.58

Answer (rounded to the nearest tenth)

The area of the roof is 1580.6 ft²