Question

A cone has a height of `24 cm` and its base has a radius of `15 cm`. If the cone is horizontally cut into two segments `18 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `2001.38(2dp) cm^2`[Ans]

Explanation:

The cone is cut at 18 cm from base, So upper radius of the frustum of cone is `r_2=(24-18)/24*15=3.75 cm` ; slant ht `l=sqrt(18^2+(15-3.75)^2)=sqrt(324+126.56)=sqrt 450.56=21.226 cm`
Top surface area `A_t=pi*3.75^2=44.179 cm^2`
Bottom surface area `A_b=pi*15^2=706.858 cm^2`
Slant Area `A_s=pi*l*(r_1+r_2)=pi*21.226*(15+3.75)=1250.342 cm^2`
Total surface area of bottom segment `=A_t+A_b+A_s=44.179+706.858+1250.342=2001.38(2dp) cm^2` [Ans]