Question

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. What is the area of the roof? What is the lateral area of the roof?

Answer 1

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

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:

A
`L`=
`15\pi \sqrt{30^(2) +15^(2) }` ≈ 1580.58 ft^2.