Question

A cone has a height of `6 cm` and its base has a radius of `4 cm`. If the cone is horizontally cut into two segments `3 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `130.80(2dp)`sq.cm

Explanation:

The cone is cut at 3 cm from base, So upper radius of the frustum of cone is `r_2=(6-3)/6*4=2 cm` ; slant ht `l=sqrt(3^2+(4-2)^2)=sqrt(9+4)=sqrt 13=3.606 cm`

Top surface area `A_t=pi*2^2=12.566 cm^2`
Bottom surface area `A_b=pi*4^2=50.265 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*3.606*(4+2)=67.971 cm^2`

Total surface area of bottom segment `=A_t+A_b+A_s=12.566+50.265+67.971=130.80(2dp)`sq.cm[Ans]