Question

The formula for the surface area of a cone is given by the formula 𝐴 = 𝜋𝑟2 + 𝜋𝑟√𝑟2 + ℎ2 , where A represents the surface area, r represents the radius, and h represents the height. If the surface area of a cone is 225 cm2 and the radius is 4 cm, find the height of the cone

Answer 1

We are given the surface area of the cone A = 225 cm^2 and the radius r = 4 cm. We are asked to find the height h of the cone.

Substitute the given values into the formula:
A = πr^2 + πr√(r^2 + h^2)

225 = π(4^2) + π(4)√(4^2 + h^2)

225 = 16π + 4π√(16 + h^2)

225 - 16π = 4π√(16 + h^2)

Divide both sides by 4π:
(225 - 16π)/(4π) = √(16 + h^2)

Square both sides:
[(225 - 16π)/(4π)]^2 = 16 + h^2

(225 - 16π)^2/(4π)^2 = 16 + h^2

Simplify the left side:
[(225 - 16π)^2/(4π)^2] = 16 + h^2

(225^2 - 2*225*16π + (16π)^2)/(4π)^2 = 16 + h^2

(225^2 - 2*225*16π + 256π^2)/(16π^2) = 16 + h^2

Now we can calculate the height h using a calculator.