Question

A cone has a height of `18 cm` and its base has a radius of `7 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 `548.52cm^2 (2dp)`

Explanation:

The cone is cut at 12 cm from base, So upper radius of the frustum of cone is `r_2=(18-12)/18*7=2.33` cm ; slant ht `l=sqrt(12^2+(7-2.3)^2)=sqrt(144+21.77)=sqrt 165.77=12.88 cm`
Top surface area `A_t=pi*2.33^2=17.06 cm^2`
Bottom surface area `A_b=pi*7^2=153.94 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*12.88*(7+2.33)=377.52cm^2`
Total surface area of bottom segment `=A_t+A_b+A_s=17.06+153.94+377.52=548.52cm^2 (2dp)`[Ans]