A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm x 14 cm x 10.5 cm. Find the rise in level of the water when the solid is submerged.
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm x 14 cm x 10.5 cm. Find the rise in level of the water when the solid is submerged.

Diameter of cylindrical container = 42 cm it’s radius (r) = 21 cm

Dimensions of rectangular solid = 22cm x 14cm x 10.5cm

The volume of solid = 22 x 14 x 10.5 cm3 ….. (i)

Let the height of water = h

So, the volume of water in the container will be

    \[\begin{array}{*{35}{l}} =~\pi {{r}^{2}}h  \\ =\text{ }22/7\text{ x }21\text{ x }21\text{ x }h\text{ }c{{m}^{3}}~\ldots \ldots \text{ }\left( ii \right)  \\ 22/7\text{ x }21\text{ x }21\text{ x }h\text{ }=\text{ }22\text{ x }14\text{ x }10.5  \\ 22\text{ x }3\text{ x }21\text{ x }h\text{ }=\text{ }22\text{ x }14\text{ x }10.5  \\ h\text{ }=\text{ }\left( 22\text{ x }14\text{ x }10.5 \right)/\text{ }\left( 22\text{ x }3\text{ x }21 \right)  \\ =\text{ }7/3\text{ }=\text{ }2.33\text{ }cm  \\ \end{array}\]

Therefore, the water level will be raised to a level of 2.33 cm when the solid is submerged.