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 V_{old} = area of base × height upto which water is filled

⇒ V_{old} = (16×16)×10

= 2560cm^{3}

Now, volume of the cube to be immersed V_{cube}= 8×8×8

⇒ V_{cube}= 512 cm^{3}

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} = 2560cm^{3}+512 cm^{3}

⇒ V_{new} = 3072 cm^{3}

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.

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