A cone has a height of 9 cm and its base has a radius of 8 cm. If the cone is horizontally cut into two segments 2 cm from the base, what would the surface area of the bottom segment be?

1 Answer
Nov 27, 2016

pi*(8*root2(145)-56/81*root2(7105))

Explanation:

The apotheme is a=root2(h^2+r^2)=root2(9^2+8^2)=root2(145)

the lateral surface area of the lower section is given by pi*(r*a-r'*a')

with r' the radius of the higher cone section, but we know that
9:8=7:r' from which r'=7*8/9=56/9

so a'=root2(49+ (56/9)^2)=root2(7105)/9

In the end
the lateral surface sought is pi(8*root2(145)-56/81*root2(7105))