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#.