Question

The volume of a right circular cone is 9856cm³.If the diameter of the base is 28cm,find.(i)height of the cone (ii)slant height of the cone(iii)curved surface area of the cone.

Answer 1

i)height=48cm ii)slant height =50cm iii)csa=2198cm

Answer 2

Given :-

The volume of the right circular cone

= 9856cm^3

Diameter =28 cm

Radius = Diameter/2

Radius of the cone = 14cm

Solution 1 :-

Volume of the cone = 1/3πr^2h

Put the required values in the formula ,

9856 = 1/3 * 22/7 * 14 * 14 * h

h = 9856 * 3 * 7 / 22 * 14 * 14

h = 206976 / 4312

h = 48

Hence , The height of the cone is 48cm

Solution 2 :-

Radius of the cone = 14 cm

Height of the cone = 48cm

Now ,

( l )^2 = (radius)^2 + ( height )^2

Slant height ( l )^2 = √( 14)^2 + ( 48)^2

( l )^2 = 196 + 2304

( l )^2 = 2500

l = 50 cm

Thus , The slant height of a cone is 50 cm

Solution 3 :-

Total surface area of cone

Put the required values in the formula ,

TSA of cone = 22/7 * 14 ( 50 + 14)

TSA of cone = 22 * 2 * 64

TSA of cone = 2816 cm²