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 the level of the water when the solid is submerged.

Given,

Diameter of base = 42 cm and radius = $\dfrac{42}{2}$ = 21 cm.

Let rise in level of water be h cm.

Since, water rises on submerging of a rectangular solid.

So, the increase in volume of water = volume of rectangular solid.

∴ πr²h = 22 x 14 x 10.5

$\dfrac{22}{7} \times 21^2 \times h$ = 3234

h = $\dfrac{3234 \times 7}{22 \times 21^2} = \dfrac{22638}{9702} = 2\dfrac{1}{3}$ cm

Hence, the water level will be raised to a level of $2\dfrac{1}{3}$ cm when the solid is submerged.