Answer
The volume of the given figure is\[150\pi \text{ c}{{\text{m}}^{3}}\]or\[471\text{ c}{{\text{m}}^{3}}\].
Work Step by Step
The diameter and height of the given figure is 10 cm and 8 cm, respectively. To compute the volume of the figure, firstly compute the volume of the upper part, which is a hemisphere. Secondly, compute the volume of the lower part, which is a cone. Finally, add the volume of both the upper and lower parts to ascertain the volume of the given figure.
Firstly, compute the radius of the given figure using the equation:
\[\begin{align}
& \text{Radius}=\left( \frac{1}{2}\times 10 \right)\text{cm} \\
& =5\text{ cm}
\end{align}\]
Compute the volume of the upper part that is hemisphere using the equation as shown below:
\[\begin{align}
& \text{Volume of the Hemisphere }\left( V \right)=\frac{2}{3}\left( \pi {{\left( 5\text{ cm} \right)}^{3}} \right) \\
& =83\pi \text{ c}{{\text{m}}^{3}}
\end{align}\]
Compute the volume of the lower part that is cone using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cone (}V\text{)}=\frac{1}{3}\left( \pi {{\left( 5\text{ cm} \right)}^{2}}8\text{ cm} \right) \\
& =67\pi \text{ c}{{\text{m}}^{3}}
\end{align}\]
Now, compute the volume of the given figure using the equation as shown below:
\[\begin{align}
& \text{Volume of the figure}=\text{Volume of upper part}+\text{Volume of lower part} \\
& \text{=}\left( 83\pi +67\pi \right)\text{c}{{\text{m}}^{3}} \\
& =150\pi \text{ c}{{\text{m}}^{3}} \\
& =471\text{ c}{{\text{m}}^{3}}
\end{align}\]
