A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid

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:

Given data is as follows:

Diameter of cylinder = 56 cm

Dimensions of rectangular block = 32 cm × 22 cm × 14 cm

We have to find the raise in the level of water in the cylinder.

First let us find the raise in the level of water in the cylinder. Diameter is given as 56 cm. Therefore,

r = 28 cm

We know that the raise in the volume of water displaced in the cylinder will be equal to the volume of the rectangular block.

Let the raise in the level of water be h. Then we have,

Volume of cylinder of height h and radius 28 cm = Volume of the rectangular block

22/7 × 28 × 28 × h = 32 × 22 × 14

h = 4 cm

Therefore, the raise in the level of water when the rectangular block is immersed in the cylinder is 4 cm.

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