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Question
A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm × 22 cm × 14 cm. Find the rise in the level of the water when the solid is completely submerged.
Solution
Diameter of the cylindrical container = d cm = 56 cm
Radius of the cylindrical container = r cm = 28 cm
Volume of cylindrical container = Volume of the rectangular solid
Length of the rectangular solid = 32 cm
Breadth of the rectangular solid = 22 cm
Height of the rectangular solid = 14 cm
Volume of the rectangular solid = Length x Breadth x Height = 32 cm x 22 cm x 14 cm = 9856 cm3
Volume of the cylindrical container = 9856 cm3 = πr2h
9856 cm3 = 22(28 cm)2h
7
h = 4 cm
Thus, when the solid is completely submerged, the water will rise up to 4 cm.
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