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?

Answer 1

To find the area of the roof, we first need to find the slant height of the cone. This can be done using the Pythagorean theorem:

h^2 = r^2 + s^2
30^2 = 15^2 + s^2
900 = 225 + s^2
s^2 = 675
s = √675
s ≈ 25.98 ft

Now, we can calculate the area of the cone using the formula:

A = πr(r + s)
A = π(15)(15 + 25.98)
A = π(15)(40.98)
A ≈ 1936.6 ft^2

Therefore, the area of the roof of the tower is approximately 1936.6 square feet.