Question

A cone has a height of `12 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `6 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `182.05(2dp)` sq,cm

Explanation:

The cone is cut at 6 cm from base, So upper radius of the frustum of cone is `r_2=(12-6)/12*4=2.0` cm ; slant ht `l=sqrt(6^2+(4-2.0)^2)=sqrt(36+4)=sqrt 40.0=6.325 cm`
Top surface area `A_t=pi*2.0^2=12.566`
Bottom surface area `A_b=pi*4^2=50.265`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*6.325*(4+2)=119.223`
Total surface area of bottom segment `=A_t+A_b+A_s=12.566+50.265+119.223=182.05(2dp)`sq,cm[Ans]