Question

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom, as shown in figure, is ______.

Answer 1

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom, as shown in figure, is `underlinebb(1/3 πr^2 (3h - 2r))` .

Explanation:

Volume of the cylinder:

`V_"cylinder" = πr^2h`

Volume of the hemisphere:

`V_"hemisphere" = 2/3 πr^2`

Total capacity of the vessel:

Capacity = `V_"cylinder" - V_"hemisphere"`

Capacity = `πr^2h - 2/3 πr^3`

Simplifying the expression:

Take `1/3 πr^2` out as a common factor:

Capacity = `1/3 πr^2 (3h - 2r)`