Question

The vwrticql height of q right circular cone is three times its diamter and its volume is 54 pie cm³. Find its height.

Answer 1

Answer:

The height of the cone is 18cm.

Step-by-step explanation:

Let the height be 'h' and the diameter be 'd'

We know that d = 2r where r is the radius of the cone.

Given that h = 3d

                    = 3(2r)

                    = 6r

We know that the Volume of the cone = $\frac{1}{3}$ * πr²h

Substituting the values, we get

54π =  $\frac{1}{3}$ * πr²(6r)

=> 162 = 6r³

=> 27 = r³

Taking cube root on both the sides

=> r = 3

Since, h = 6r

=> h = 6*3

=> h =18

Therefore, the height of the cone is 18cm.