Question

A cone has a height of `32 cm` and its base has a radius of `18 cm`. If the cone is horizontally cut into two segments `12 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `2680.67(2dp) cm^2`

Explanation:

The cone is cut at 12 cm from base, So upper radius of the frustum of cone is `r_2=(32-12)/32*18=11.25` cm ; slant ht `l=sqrt(12^2+(18-11.25)^2)=sqrt(144+45.56)=sqrt 189.56=13.77 cm`

Top surface area `A_t=pi*11.25^2=397.61 cm^2`
Bottom surface area `A_b=pi*18^2=1017.88 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*13.77*(18+11.25)=1265.18 cm^2`

Total surface area of bottom segment `=A_t+A_b+A_s=397.61+1017.88+1265.18=2680.67(2dp) cm^2`[Ans]