Question

A hemisphere is placed on top of a cylinder with the same radius. The height of the cylinder is 10 inches and the radius is 3 inches.What is the volume of this composite figure? Use the \piπ button on your calculator to determine the answer. Round your answer to the hundredths place.

Answer 1

Given,

The radius of the cylinder and the hemisphere, r=3 inches

The height of the cylinder, h=10 inches.

The volume of the whole figure is the sum of the volume of the cylinder and the volume of the hemisphere.

Hemisphere is the half of a sphere. Thus the volume of a hemisphere is equal to half of the volume of the sphere with the same radius as the hemisphere.

The volume of the given hemisphere is,

$V_h=\frac{2}{3}\pi r^3$

On substituting the known values,

$\begin{gathered} V_h=\frac{2}{3}\pi\times3^3 \\ =56.55\text{ cubic inches} \end{gathered}$

The volume of the cylinder is given by,

$V_c=\pi r^2h$

On substituting the known values,

$\begin{gathered} V_c=\pi\times3^2\times10 \\ =282.74\text{ cubic inches} \end{gathered}$

Thus the total volume of the given figure is,

$\begin{gathered} V=V_h+V_c \\ =56.55+282.74 \\ =339.29\text{ cubic inches} \end{gathered}$

Thus the volume of the given figure is 339.29 cubic inches