 # Question

A solid with a square base of edge 11 cm and volume of 1573 cm3 was placed in a tank with its base touching the base of the tank.

The volume of the water in the tank is 80 by 60 by 23

The water level in the tank was 23 cm. The tap attached to the tank was turned on and water flowed out at a rate of 3 litre per minute.

A) How long does it take for the water level just to reach the top of the solid?

B) The tap was then turned off. What will the height of the water level be when the solid was then removed from the tank? (Give your answer correct to 2 decimal places.)

Source: Maha Bodhi

Height of square-based solid of edge 11 cm = 1573 / (11×11) = 13 cm

Height of water level to be drained to reach the top of solid = 23 – 13 = 10 cm

Volume of water to be flowed out of tank to reach the top of solid = 80 x 60 x 10 = 48000 cm3

Time taken for the water to flow out at 3 l/min to reach the top of solid = 48000/3000 = 16 min

Volume of water in tank with solid inside = 80 x 60 x 13 = 62400 cm3

Volume of water in tank when solid is removed = 62400 – 1573 = 60827 cm3

Height of water level when solid is removed = 60827 / (80 x 60) = 12.67 cm

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