The material of a solid right circular cylinder is converted into the shape of a solid cone of equal radius. If the height of the cylinder was 4.5 cm, then the height of the cone is:

When an object is recast or converted into another shape, its total volume remains constant.
Volume of Cylinder=Volume of Cone
Let the common radius of both shapes be r.
Let the height of the cylinder be h
cylinder
​
=4.5 cm.
Let the height of the cone be h
cone
​
.

Formulas:

Volume of Cylinder=πr
2
h
cylinder
​

Volume of Cone=
3
1
​
πr
2
h
cone
​

Equating both volumes:

πr
2
h
cylinder
​
=
3
1
​
πr
2
h
cone
​

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

h
cylinder
​
=
3
1
​
h
cone
​

4.5=
3
1
​
h
cone
​

h
cone
​
=4.5×3=13.5 cm