A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height so that the solid is completely submerged in water. If the radius of the cylinder is 14 cm, find the rise in the water level.

Let the rise in water level be x cm.

∴ Volume of water that rises by x cm in the cylindrical container = Volume of hemisphere submerged + Volume of cone submerged

⇒ π × (14)² × x = $\dfrac{2}{3} \times π \times 7^3 + \dfrac{1}{3} \times π \times 7^2 \times 4$

⇒ 196πx = $\dfrac{2}{3} \times π \times 343 + \dfrac{1}{3} \times π \times 196$

⇒ 196x = $\dfrac{2}{3} \times 343 + \dfrac{1}{3} \times 196$

⇒ 196x = $\dfrac{686 + 196}{3}$

⇒ 196x = $\dfrac{882}{3}$

⇒ x = $\dfrac{882}{3 \times 196} = \dfrac{882}{588}$ = 1.5 cm.

Hence, rise in water level = 1.5 cm