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 = ?
First we will find the Volume of water filled in the prism before immersing the cube.
So, Volume of water Vold = area of base × height upto which water is filled
⇒ Vold = (16×16)×10
Now, volume of the cube to be immersed Vcube= 8×8×8
⇒ Vcube= 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, Vnew = Vold+ Vcube
⇒ Vnew = 2560cm3+512 cm3
⇒ Vnew = 3072 cm3
Now, this new volume will have an increase in height.
So to find the new height of water level,
⇒ Vnew = area of base × new height upto which water is filled
⇒ 3072 = 16×16×h
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
∴ The water rose by 2cm after immersing the cube in the prism.
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