Question

A cone has a height of `24 cm` and its base has a radius of `14 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

Total surface area of bottom segment is `1416.76` sq.cm.

Explanation:

The cone is cut at `4` cm from base, So upper radius of the

frustum of cone is `r_2=(24-4)/24*14~~ 11.67`cm ;

Slant height: `l=sqrt(4^2+(14-11.67)^2)~~4.63` cm

Top surface area `A_t=pi*11.67^2 ~~427.61` sq.cm

Bottom surface area `A_b=pi*14^2~~615.75` sq.cm

Slant Area: `A_s=pi*l*(r_1+r_2)=pi*4.63*(14+11.67)`

`~~373.40` sq.cm. Total surface area of bottom segment

`A=A_t+A_b+A_s=427.61+615.75+373.40`

`~~ 1416.76 (2dp)` sq.cm [Ans]