Answer
Volume is\[324\pi \text{ c}{{\text{m}}^{3}}\]or\[1,018\text{ c}{{\text{m}}^{3}}\].
Work Step by Step
The diameter and height of the given figure is 12 cm and 15 cm, respectively.In order 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:
\[\begin{align}
& \text{Radius}=\left( \frac{1}{2}\times 12\text{ cm} \right) \\
& =6\text{cm}
\end{align}\]
Compute the volume of the upper part that is hemisphere using the equation as shown below:
\[\begin{align}
& \text{Volume of the Hemisphere}\left( V \right)=\frac{2}{3}\left( \pi {{\left( 6\text{ cm} \right)}^{3}} \right) \\
& =144\pi \text{c}{{\text{m}}^{3}}
\end{align}\]
Compute the volume of the lower part that is cone using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cone (}V\text{)}=\frac{1}{3}\left( \pi {{\left( 6\text{ cm} \right)}^{2}}15\text{ cm} \right) \\
& =180\pi \text{ c}{{\text{m}}^{3}}
\end{align}\]
Now, compute the volume of the given figure using the equation as shown below:
\[\begin{align}
& \text{Volume of the figure}=\text{Volume of upper part}+\text{Volume of lower part} \\
& \text{=}\left( 144\pi +180\pi \right)\text{c}{{\text{m}}^{3}} \\
& =324\pi \text{ c}{{\text{m}}^{3}} \\
& =1018\text{ c}{{\text{m}}^{3}}
\end{align}\]
