If a cylinder of radius 7cm and height 9cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

When an object is melted and recast into another shape, its total volume remains unchanged.
Volume of Cylinder=Volume of Cone
Let the radius of the cylinder be r=7cm and height be h
cyl
​
=9cm.
Let the radius of the cone be r=7cm and height be h
cone
​
.

πr
2
h
cyl
​
=
3
1
​
πr
2
h
cone
​

Since the radii are identical, πr
2
cancels out from both sides:

h
cyl
​
=
3
1
​
h
cone
​

9=
3
1
​
h
cone
​

h
cone
​
=9×3=27cm