A hollow prism of base a square of side 16 centimetres contains water 10 centimetres high. If a solid cube of side 8 centimetres is immersed in it, by how much would the water level rise?

Given: side of base of the prism “s” = 16cm

Water is filled upto height “h” = 10cm

Side of cube “c” = 8cm

To find : rise in water level after inserting the cube in the prism = ?

Procedure :

First we will find the Volume of water filled in the prism before immersing the cube.

So, Volume of water V_old = area of base × height upto which water is filled

⇒ V_old = (16×16)×10

= 2560cm³

Now, volume of the cube to be immersed V_cube= 8×8×8

⇒ V_cube= 512 cm³

Now, after immersing the cube, the total volume in which the water is present will be = old volume of water + volume of cube

So, V_new = V_old+ V_cube

⇒ V_new = 2560cm³+512 cm³

⇒ V_new = 3072 cm³

Now, this new volume will have an increase in height.

So to find the new height of water level,

⇒ V_new = area of base × new height upto which water is filled

⇒ 3072 = 16×16×h

⇒ h=

=

= 12cm

Now we have,

⇒ Old height upto which the water was present in the prism = 10cm

⇒ New height upto which the water was present in the prism = 12cm

∴ increase in height of water = 12-10

= 2cm

∴ The water rose by 2cm after immersing the cube in the prism.