Question

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find

1. height of the cone
2. slant height of the cone
3. curved surface area of the cone

`["Assume "pi=22/7]`

Answer 1

(i) Radius of cone = `(28/2) cm` = 14 cm

Let the height of the cone be h.

Volume of cone = 9856 cm³

⇒ `1/3pir^2h` = 9856 cm³

⇒ `[1/3xx22/7xx(14)^2xxh]cm^2` = 9856 cm³

h = 48 cm

Therefore, the height of the cone is 48 cm.

(ii) Slant height (l) of cone = `sqrt(r^2+h^2)`

= `[sqrt(14^2+48^2)]cm`

= `[sqrt(196+2304)]cm`

= 50 cm

Therefore, the slant height of the cone is 50 cm.

(iii) Curved surface area of cone = πrl

= `(22/7xx14xx50)cm^2`

= 2200 cm²

Therefore, the curved surface area of the cone is 2200 cm².