Mathematics
A rectangular tank 30 cm x 20 cm x 12 cm contains water to a depth of 6 cm. A metal cube of side 10 cm is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in litres, that must be poured in the tank so that the metal cube is just submerged in the water.
Answer
Given:
Dimensions of the tank = 30 cm x 20 cm x 12 cm
Side of the cube = 10 cm
Initial depth of water in the tank = 6 cm
Initial volume of water in tank = 30 x 20 x 6 = 3600 cm3
Volume of cube = side cm3 = 10 x 10 x 10 = 1000 cm3
Volume of water required to fill the tank to a depth of 10 cm = 30 x 20 x 10 = 6000 cm3
Additional volume of water required to just submerge the cube = Volume of water at 10 cm depth - Volume of water at 6 cm depth - Volume of cube
= 6000 - 3600 - 1000
= 1400 cm3 = 1.4 litre
Hence, the volume of water that must be poured into the tank so that the metal cube is just submerged is 1.4 litre.
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