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Question

A hollow prism with a square base of side 16 cm contains water, which is 10 cm high. If a solid cube of side 8 cm is immersed in it, what will be the new height of water level in the prism?

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Solution

Volume of the solid cube = Volume of the water displaced in the prism

Let the rise in water level/ height of water displaced in the prism = x cm

Side of the hollow prism base = 16 cm

Initial height of water level in the prism = 10 cm

Area of the base of hollow prism = s2 = 16×16

=256 cm2

Volume of the solid cube = Area of base of hollow prism×height of the water displaced in the prism

8×8×8=256×x

x=8×8×8256=2 cm

Height of water displaced = level by which water rises = 2 cm

New height of water in the hollow prism = (10+2) = 12 cm


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