Question

A cone has a height of `24 cm` and its base has a radius of `9 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 `652.62` sq.cm

Explanation:

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

cone is `r_2=(24-4)/24*9=7.5`cm ; slant ht

`l=sqrt(4^2+(9-7.5)^2)=sqrt(16+2.25)=sqrt 18.25 ~~ 4.27` cm

Top surface area `A_t=pi*7.5^2 ~~ 176.71` sq.cm

Bottom surface area `A_b=pi*9^2 ~~254.47` sq.cm

Slant Area `A_s=pi*l*(r_1+r_2)=pi*4.27*(9+7.5) ~~ 221.44`

Total surface area of bottom segment

`=A_t+A_b+A_s=176.71+254.47+221.44 ~~ 652.62` sq.cm[Ans]