Q. 34.2( 9 Votes )

A hollow prism of

Answer :

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 Vold = area of base × height upto which water is filled


Vold = (16×16)×10


= 2560cm3


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


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.


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