Question

A hemispherical bowl of internal radius 9 cm is full of water. Its contents are emptied in a cylindrical vessel of internal radius 6 cm. Find the height of water in the cylindrical vessel.

Answer 1

Let the height of water in the cylindrical vessel be h cm.

Given: Radius of the hemispherical bowl, r = 9 cm

∴ Volume of the water in hemispherical bowl, `V_1=pi2/3r^3`

`V_1=pi2/3xx(9cm)`

Given: Radius of the cylinder, R = 6 cm,

∴ Volume of water in the cylindrical vessel, V₂ = π r²h

⇒ V₂ = π (6 cm)² h

Since water is emptied from the hemispherical bowl into the cylindrical vessel,

∴Volume of water in cylindrical vessel = Volume of the water in hemispherical bowl

`rArrpi(6)^2h=2/3pi(9)^3`

`rArrh=(2xx(9)^3)/(3xx(6)^2)`

`rArrh=27/2`

`rArrh=13.5`

Thus, the height of water in the cylindrical vessel is 13.5 cm.