Question

A cone has a height of `16 cm` and its base has a radius of `15 cm`. If the cone is horizontally cut into two segments `4 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

The surface area of the bottom segment is `1583.36cm^2`.

Explanation:

This is a truncated cone where the top segment is removed.

Let `R=15` and `h=4`,

`r=(16-4)/16xx15`
`color(white)(r)=12`

`"Surface area"=pi(r+R)(sqrt((r-R)^2+h^2))+pir^2+piR^2`
`color(white)"Surface area"=pi(12+15)(sqrt((12-15)^2+4^2))+pi(12)^2+pi(15)^2`
`color(white)"Surface area"=pi(27)(5)+pi(144)+pi(225)`
`color(white)"Surface area"=1583.36`

The surface area of the bottom segment is `1583.36cm^2`.