How do I find the lateral area of a cone with just the height and diameter?

Question

I have to find a lateral area of a con whose height is 32 cm and whose diameter is 28 cm. There’s a hint that tells me to use the Pythagorean theorem to calculate the slant height..

Answer 1

The lateral area of a cone is given by the following formula,

Area = πr√(h^2 + r^2)

[Note that r = 14 since the diameter is 28]

Plugging in the values given by the problem, we get

Area = π(14)√((32)^2 + (14)^2)

Area = 14π√(1024 + 196)

Area = 14π√(1220)

Area ≈ 14π(34.9)

Area ≈ 1536.2