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Question

# A rectangular tank 30 cm×20 cm×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 liters, that must be poured in the tank so that the metal cube is just submerged in water.

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Solution

## To solve this problem, we must make some assumptions: 1) The height of the tank is the 12 cm 2) The metal cube is already in the tank when the 6 cm water depth is measured to cover the cube with water we need another 4 cm of water depth:Height of cube − height of water already in tank =10−6=4 cmVolume of cuboidal shape =length×breadth×height,V=l×b×h The additional volume of water needed to cover the cube:V=30×20×4 but the cube will displace some of that water, so we only need:V=30×20×4−10×10×4=2000 cm3=2000×(11000) litre [1 litre =1000 cm3, 1 cm3=11000 cm3]=2 liters

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