Question

A cone has a height of `8 cm` and its base has a radius of `5 cm`. If the cone is horizontally cut into two segments `6 cm` from the base, what would the surface area of the bottom segment be?

Answer 1

Total surface area of bottom segment is `222.38` sq.cm

Explanation:

The cone is cut at 6 cm from base, So upper radius of the frustum

of cone is `r_2=(8-6)/8*5=1.25` cm ; Slant ht

`l=sqrt(6^2+(5-1.25)^2)=sqrt(36+14.0625)`

`=sqrt 50.0625 ~~ 7.08` cm

Top surface area `A_t=pi*1.25^2 ~~ 4.91`sq.cm

Bottom surface area `A_b=pi*5^2 ~~ 78.54` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*7.08*(5+1.25)`

`~~138.93` sq.cm

Total surface area of bottom segment

`=A_t+A_b+A_s=4.91+78.54+138.93`

`~~ 222.38` sq.cm [Ans]