Answer
The volume of the given figure is\[\frac{3,332}{3}\pi \text{ }{{\text{m}}^{3}}\]or\[3,489\text{ }{{\text{m}}^{3}}\].
Work Step by Step
The diameter and height of the lower part, which is a cylinder are 14m and 18m respectively. The diameter of the upper part, which is a sphere is 14m.
In order to compute the volume of the figure, firstly compute the volume of the upper part, which is a sphere. Secondly, compute the volume of the lower part which is a cylinder. Finally, add the volume of both the upper and lower parts to ascertain the volume of the given figure.
Compute the radius of the given figure using the equation:
\[\begin{align}
& \text{Radius}=\left( \frac{1}{2}\times 14\text{ m} \right) \\
& =7\text{ m}
\end{align}\]
Compute the volume of the upper part that is hemisphere using the equation as shown below:
\[\begin{align}
& \text{Volume of the Hemispherical part }\left( V \right)=\frac{2}{3}\pi {{r}^{3}} \\
& =\frac{2}{3}\left( \pi {{\left( 7\text{ m} \right)}^{3}} \right) \\
& =\frac{686}{3}\pi \text{ }{{\text{m}}^{3}}
\end{align}\]
Compute the volume of the lower part that is cylinder using the equation as shown below:
\[\begin{align}
& \text{Volume of the cylindrical part (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 7\text{ m} \right)}^{2}}18\text{ m} \right) \\
& =882\pi \text{ }{{\text{m}}^{3}}
\end{align}\]
Now, compute the volume of the given figure using the equation as shown below:
\[\begin{align}
& \text{Volume of the figure}=\text{Volume of upper part}+\text{Volume of lower part} \\
& \text{=}\left( \frac{686}{3}\pi +882\pi \right){{\text{m}}^{3}} \\
& =\frac{3,332\pi }{3}{{\text{m}}^{3}} \\
& =3849\text{ }{{\text{m}}^{3}}
\end{align}\]s
