Answer
The volume of the cylinder is\[588\pi \text{ c}{{\text{m}}^{3}}\text{ or }1,847\text{ c}{{\text{m}}^{3}}\].
Work Step by Step
The diameter and height of the cylinder is 14 cm and 12 cm, respectively. The volume of the cylinder will be computed by multiplying the square of the radius with the height and finally multiplying the resultant with the value of pie.
Firstly, compute the radius of the cylinder using the equation:
\[\begin{align}
& \text{Radius}=\frac{\text{1}}{\text{2}}\times \text{Diameter} \\
& =\left( \frac{1}{2}\times 14 \right)\text{cm} \\
& =7\text{cm}
\end{align}\]
Compute the volume of the cylinder using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cylinder (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 7\text{ cm} \right)}^{2}}12\text{ cm} \right) \\
& =588\pi \text{ c}{{\text{m}}^{3}} \\
& =1,847\text{ c}{{\text{m}}^{3}}
\end{align}\]