Question

A cone has a height of `24 cm` and its base has a radius of `9 cm`. If the cone is horizontally cut into two segments `15 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `913.07(2dp)` sq.cm.

Explanation:

The cone is cut at 15 cm from base, So upper radius of the frustum of cone is `r_2=(24-15)/24*9=3.375` cm ; Slant height `l=sqrt(15^2+(9-3.375)^2)=sqrt(225+31.64)=sqrt 256.64=16.02 cm`

Top surface area `A_t=pi*3.375^2=35.785 sq.cm`
Bottom surface area `A_b=pi*9^2=254.469 sq.cm`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*16.02*(9+3.375)=622.813sq. cm`

Total surface area of bottom segment `=A_t+A_b+A_s=35.785+254.469+622.813=913.07(2dp)`sq.cm[Ans]