Question

A cone has a height of `15 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `10 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `229.26(2dp)`sq.cm

Explanation:

The cone is cut at 10 cm from base, So upper radius of the frustum of cone is `r_2=(15-10)/15*4=1.333` cm ; slant ht `l=sqrt(10^2+(4-1.33)^2)=sqrt(100+7.11)=sqrt 107.11=10.349`cm.

Top surface area `A_t=pi*1.33^2=5.585` sq.cm
Bottom surface area `A_b=pi*4^2=50.265` sq.cm
Slant Area `A_s=pi*l*(r_1+r_2)=pi*10.349*(4+1.33)=173.406` sq.cm

Total surface area of bottom segment `=A_t+A_b+A_s=5.585+50.265+173.406=229.26(2dp)`sq.cm[Ans]