Question

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?

Answer 1

`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))`