A vessel is in the shape of a square prism, with each side of the base 16 centimetres long. It contains water 10 centimetres high. If a cube of side 8 centimetres is completely immersed in it, how high would the water level rise?

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Solution

Side of the base of the square prism = 16 cm

Area of the base of the square prism = Side × Side

= (16 × 16) cm²

= 256 cm²

Height of the water level = 10 cm

Quantity of water in the vessel = Base area × Height of water

= 256 × 10 cm³

= 2560 cm³

Length of side of cube immersed in the vessel = 8 cm

Volume of the cube = Side × Side × Side

= 8 × 8 × 8 cm³

= 512 cm³

∴ New volume of water in the vessel = (2560 + 512) cm³

= 3072 cm³

⇒ Base area × New height = 3072

⇒ 256 cm²× New height = 3072 cm³

⇒ New height =

∴ Increase in the water level = (12 − 10) cm = 2 cm

Thus, the water level will rise by 2 cm.

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