Answer
The volume of the given figure is\[432\pi \text{ in}{{\text{.}}^{3}}\]or\[1,357\text{ i}{{\text{n}}^{3}}\].
Work Step by Step
The diameter and height of the lower part, which is a cylinder is 12 inches and 11 inches,respectively. The diameter and height of the upper part, which is a cone is 12 inches and 3 inches. The height of the conical part has been computed by deducting the height of the cylindrical part from the total height of the given figure.
In order to compute the volume of the figure, firstly compute the volume of the upper part, which is a cone. 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:
\[\begin{align}
& \text{Radius}=\frac{\text{1}}{\text{2}}\times \text{Diameter} \\
& =\left( \frac{1}{2}\times 12\text{ in}\text{.} \right) \\
& =6\text{ in}\text{.}
\end{align}\]
Compute the volume of the upper part that is hemisphere using the equation as shown below:
\[\begin{align}
& \text{Volume of the Conical part (}V\text{)}=\frac{1}{3}\pi {{r}^{2}}h \\
& =\frac{1}{3}\left( \pi {{\left( 6\text{ in}\text{.} \right)}^{2}}3\text{ in}\text{.} \right) \\
& =36\pi \text{ in}{{\text{.}}^{3}}
\end{align}\]
Compute the volume of the lower part that is cylinder using the equation as shown below:
\[\begin{align}
& \text{Volume of the cylindrical part (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 6\text{ in}\text{.} \right)}^{2}}11 \right)\text{in}{{\text{.}}^{3}} \\
& =396\pi \text{ in}{{\text{.}}^{3}}
\end{align}\]
Now, compute the volume of the given figure using the equation as shown below:
\[\begin{align}
& \text{Volume of the figure}=\text{Volume of upper part}+\text{Volume of lower part} \\
& \text{=}\left( 36\pi +396\pi \right)\text{ i}{{\text{n}}^{3}} \\
& =432\pi \text{ i}{{\text{n}}^{3}} \\
& =1,357\text{ i}{{\text{n}}^{3}}
\end{align}\]
