A cylindrical container with diameter of base 56 cm
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

$9856 \mathrm{~cm}^{3}=\frac{22}{7}(28 \mathrm{~cm})^{2} h$

= 4 cm

Thus, when the solid is completely submerged, the water will rise up to 4 cm.

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