Question

A cone has a height of `16 cm` and its base has a radius of `6 cm`. If the cone is horizontally cut into two segments `3 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

`color(indigo)(T_S = pi (1.125)^2 + pi 6^2 + pi * 17.09 * (6 + 1.125) = 499.61 " " cm^2`

Explanation:

`H = 16cm, h = 3cm, R = 6cm, r = (h / H ) * R = (3/16) * 6 = 1.125 cm`

`s = sqrt(H^2 + R^2) = sqrt(16^2 + 6^2) = 17.09cm`

`"Surface Area " = T_S = pir^2 + piR^2 + pi s (R + r)`

`color(indigo)(T_S = pi (1.125)^2 + pi 6^2 + pi * 17.09 * (6 + 1.125) = 499.61 " " cm^2`