Question

height of cone is 8metre and CSA of cone 188.4metre square find it's volume of cone

Answer 1

Answer:

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√(r2 + h2 ) = 188.4             {since slant height l = √(r2 + h2 )}

=> 3.14*r√(r2 + 82 ) = 188.4

=> r√(r2 + 64 ) = 188.4/3.14

=> r√(r2 + 64 ) = 60

=> r2 *(r2 + 64 ) = (60)2

=> r4 + 64r2 = 3600

=> r4 + 64r2 - 3600 = 0

=> (r2 - 36)*(r2 + 100) = 0

=> r2 = 36, -100

Since square of a number can not be negative.

Hense, r2 = -100 is not possible

So, r2 = 36

=> r = 6

Again since radius can not be negative.

So, r = 6

Now volume of the cone = (1/3)*πr2 h

                                 = (1/3)*π*62 h

                                 = (3.41*36*8)/3

                                 = 3.41*12*8

                                 = 301.44 cm3