A cone of radius 3.5cm and height 12cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 7cm. What will be the height of water in this vessel?

The volume of water remains constant when transferred from the cone to the cylinder.
Volume of the cone (V
cone
​
):

V
cone
​
=
3
1
​
πr
1
2
​
h
1
​

Given: r
1
​
=3.5cm=
2
7
​
cm, and h
1
​
=12cm.

V
cone
​
=
3
1
​
π(
2
7
​
)
2
×12=
3
1
​
π×
4
49
​
×12=49πcm
3

Volume of water in the cylinder (V
cylinder
​
):

V
cylinder
​
=πr
2
2
​
h
2
​

Given: r
2
​
=7cm and h
2
​
is the required height of water.

V
cylinder
​
=π(7)
2
h
2
​
=49πh
2
​

Equating the two volumes:

V
cylinder
​
=V
cone
​

49πh
2
​
=49π
h
2
​
=1cm
Thus, the height of the water in the cylinder will be 1cm.