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Question
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in the level of the water when the solid is submerged.
Solution
Diameter of cylindrical container = 42 cm
Therefore, radius (r) = 21 cm
Dimensions of rectangular solid = 22 cm × 14 cm × 10.5 cm
Volume of solid = 22 × 14 × 10.5 cm3 ...(1)
Let height of water = h
Therefore, volume of water in the container = πr2h
= `22/7 xx 21 xx 21 xx h cm^3`
= 22 × 63h cm3 ...(2)
From (1) and (2)
22 × 63h = 22 × 14 × 10.5
`=> h = (22 xx 14 xx 10.5)/(22 xx 63)`
`=> h = 7/3`
`=> h = 2 1/3` or 2.33 cm
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