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?

Answer 1

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 = $s^2$ = $16\times 16$

$=256c{m}^2$

Volume of the solid cube = $\text{Area of base of hollow prism}\times \text{height of the water displaced in the prism}$

$8\times 8\times 8=256\times x$

$x=\frac{8\times 8\times 8}{256}=2cm$

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

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