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 `15 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `2795.38(2dp)` sq.cm.

Explanation:

The cone is cut at 15 cm from base, So upper radius of the frustum of cone is `r_2=(32-15)/32*18=9.5625`cm ; slant ht `l=sqrt(15^2+(18-9.5625)^2)=sqrt(225+71.19)=sqrt 296.19=17.21` cm.

Top surface area `A_t=pi*9.5625^2=287.27` sq.cm
Bottom surface area `A_b=pi*18^2=1017.88`sq.cm
Slant Area `A_s=pi*l*(r_1+r_2)=pi*17.21*(18+9.5625)=1490.23`sq.cm

Total surface area of bottom segment `=A_t+A_b+A_s=287.27+1017.88+1490.23=2795.38(2dp)`sq,cm[Ans]