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?

1 Answer
Nov 18, 2017

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

Explanation:

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

http://math.tutorvista.com/geometry/cone.html

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.