Question

A cone has a height of `6 cm` and its base has a radius of `2 cm`. If the cone is horizontally cut into two segments `5 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `51.55` sq.cm.

Explanation:

The cone is cut at 5 cm high from base, So upper radius of the

frustum of cone is `r_2=(6-5)/6*2=1/3 =0.33`cm ;

Slant height of the frustum of cone is

`l=sqrt(5^2+(2-1/3)^2)=sqrt(25+2.78)~~5.27` cm

Top surface area `A_t=pi*0.33^2 ~~0.35` sq.cm

Bottom surface area `A_b=pi*2^2=12.57` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*5.27*(2+0.33)~~38.63` sq.cm

Total surface area of bottom segment is

`=A_t+A_b+A_s=0.35+12.57+38.63 ~~51.55 (2dp)`

sq.cm [Ans]