Mathematics
A rectangular container has base of length 12 cm and width 9 cm. A cube of edge 6 cm is placed in the container and then sufficient water is filled into it so that the cube is just submerged. Find the fall in level of the water, in the container, when the cube is removed.
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Answer
Given:
Length of container = 12 cm
Width of container = 9 cm
Edge of cube = 6 cm
Water is poured until the cube is just submerged.
So, the volume of water displaced = volume of the cube.
Volume of cube = 63 = 216 cm3
When the cube is removed, 216 cm³ of water is removed, causing the water level to fall.
Let the fall in water level be h cm.
Volume = Base Area × Height
108 × h = 216 (Since base area = 12 × 9 = 108 cm2)
⇒ h = = 2 cm
Hence, the fall in the level of the water = 2 cm.
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