Question

A cone of height 8 metre has a curved surface area 188.4 square metres then its volume is what ?

Answer 1

Given, height of the cone h = 8

Let r is the radius and l is the slant height of the cone.

Given curved surface area of the cone = 188.4

=> πrl = 188.4

=> πr√(r^2 + h^2 ) = 188.4 {since slant height l = √(r^2 + h^2 )}

=> 3.14*r√(r^2 + 82 ) = 188.4

=> r√(r^2 + 64 ) = 188.4/3.14

=> r√(r^2 + 64 ) = 60

=> r^2 *(r^2 + 64 ) = (60)^2

=> r^4 + 64r^2 = 3600

=> r^4 + 64r^2 - 3600 = 0

=> (r^2 - 36)*(r^2 + 100) = 0

=> r^2 = 36, -100

Since square of a number can not be negative.

Hense, r^2 = -100 is not possible

So, r^2 = 36

=> r = ±6

Again since radius can not be negative.

So, r = 6

Now volume of the cone = (1/3)*πr^2 h

= (1/3)*π*r^2*h

= (3.41*36*8)/3

= 3.41*12*8

= 301.44 cm^3