Question

A cone has a height of `27 cm` and its base has a radius of `12 cm`. If the cone is horizontally cut into two segments `4 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `1086.15` sq.cm

Explanation:

The cone is cut at `4` cm from base, So upper radius of the

frustum of cone is `r_2=(27-4)/27*12~~ 10.22(2dp)`cm.

Slant height `l=sqrt(4^2+(12-10.22)^2)=sqrt(16+3.17)`

`=sqrt 19.17 ~~4.38` cm

Top surface area `A_t=pi*10.22^2~~328.13`sq.cm

Bottom surface area `A_b=pi*12^2~~452.39` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*4.38*(12+10.22)`

`~~305.62` sq.cm. Total surface area of bottom segment

is `T_(SA)=A_t+A_b+A_s=328.13+452.39+305.62`

`~~1086.15(2dp)` sq.cm[Ans]