Question

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

Answer 1

From the given figure, the radius of the hemispherical portion is same as the radius of the cylinder.

Capacity of the cylindrical vessel with a hemispherical portion raised upward at the bottom

= Volume of the cylinder − Volume of the hemisphere

$$\begin{gathered} =\mathrm{\pi }{r}^{2}h-\frac{2}{3}\mathrm{\pi }{r}^3 \\ =\mathrm{\pi }{r}^2\left(h-\frac{2}{3}r\right) \\ =\frac{1}{3}\mathrm{\pi }{r}^2\left(3h-2r\right) \end{gathered}$$

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the following figure is $\underline{\frac{1}{3}\mathrm{\pi }{r}^2\left(3h-2r\right)}$.