The volume of a right circular cone is 9856 cm^{3}. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone

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

Advertisement Remove all ads

#### Solution

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

Let the height of the cone be *h*.

Volume of cone = 9856 cm^{3}

`rArr1/3pir^2h = 9856 cm^3`

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

*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) CSA of cone = π*rl*

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

= 2200 cm^{2}

Therefore, the curved surface area of the cone is 2200 cm^{2}.

Concept: Volume of a Right Circular Cone

Is there an error in this question or solution?

#### APPEARS IN

Advertisement Remove all ads