The roof of a tower in a castle is shaped like a cone and the base of the roof was constructed.

The height of the roof is 30ft and the radius of the base is 15ft. What is the area of the roof?

1 answer

To find the area of the roof, we first need to find the slant height of the cone using the Pythagorean theorem.

The slant height, l, can be found using the formula l = sqrt(radius^2 + height^2)

l = sqrt(15^2 + 30^2)
l = sqrt(225 + 900)
l = sqrt(1125)
l ≈ 33.54 ft

Next, we can calculate the area of the cone using the formula A = πr(l + r), where r is the radius of the base.

A = π*15*(33.54 + 15)
A = π*15*48.54
A ≈ 2283.52 ft^2

Therefore, the area of the roof is approximately 2283.52 square feet.