If a cylinder of radius 4cm and height 8cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

When a solid object is melted and recast into another solid object, its volume remains the same.
Let the radius of the cylinder be r=4cm and height be h
cylinder
​
=8cm.

The radius of the cone is also r=4cm. Let its height be h
cone
​
.

Volume of Cylinder=Volume of Cone
πr
2
h
cylinder
​
=
3
1
​
πr
2
h
cone
​

Since the radius r is identical for both, we can cancel out πr
2
from both sides:

h
cylinder
​
=
3
1
​
h
cone
​

8=
3
1
​
h
cone
​

h
cone
​
=8×3=24cm