Answer to Question #269331 in Geometry for Dondon

Question

A hemispherical container contains water to a depth of 10 cm. If the volume of the water inside the container is 5000m/3 cubic centimeter, find the diameter of the vessel.

Answer 1

The volume of water = (5000 *$\pi$)/3 cm³

The water is contained to a depth of 10 cm

Let radius of hemisphere be R₁ cm

Let radius of the water be R₂ cm

Now volume of water = (2/3)*($\pi$)*(radius)³

(5000 * $\pi$)/3 = (2/3)*($\pi$)*(R₂)³

(R₂)³ = 5000/2 = 2500 => R₂ = cube root (2500) = 13.5 cm

Now as per the diagram, AC = AD

AB + BC = R₁ (Since AD = radius of hemisphere which is R₁)

10 + R₂ = R₁

R₁ =10 + 13.5 = 23.5 cm

So,

diameter of hemisphere = 2 * radius = 2 * 23.5 = 47 cm