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 the 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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Solution

The correct option is A $2$ cm
Given $\Rightarrow$
$l = 12 c m, b = 9 c m$
height of water =side of cube $= 6 c m$

total volume occupied =volume of cube +volume of water

so,
$l b h = s^{3} + v o l o f w a t e r$
$12 \times 9 \times 6 = 6^{3} + v o l . o f w a t e r$
vol. of water $= 6 \times 6 (2 \times 9 - 6)$

In cuboid,

Volume of water (when cube is not inserted) $= l b h$
$6 \times 6 (2 \times 9 - 6)$ $= 12 \times 9 \times h$

$h = 4 c m$

so decrease in water level $= 6 - 4 = 2 c m$

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