Answer
The volume of the cone is\[15\pi \text{ y}{{\text{d}}^{3}}\text{ or }47\text{ y}{{\text{d}}^{3}}\].
Work Step by Step
The diameter and height of the cone is 6 yd. and 5 yd., respectively. The radius and height of the cone are 5 m and 16 m, respectively. The volume of the cone will be computed multiplying by the square of the radius with the height and finally multiply the resultant with the value of pie. Now, multiply the final resultant figure with one-third to get the volume of a right circular cone.
Firstly, compute the radius of the cone using the equation:
\[\begin{align}
& \text{Radius}=\left( \frac{1}{2}\times 6 \right)\text{yd} \\
& =3\text{ yd}
\end{align}\]
Compute the volume of the cone using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cone }\left( V \right)=\frac{1}{3}\left( \pi {{\left( 3\text{ yd} \right)}^{2}}5\text{ yd} \right) \\
& =\frac{1}{3}\left( \pi \times 9\text{y}{{\text{d}}^{2}}\times 5\text{ yd} \right) \\
& =\frac{1}{3}\times \left( 45\pi \right)\text{y}{{\text{d}}^{3}}
\end{align}\]
Further simplified to get:
\[\begin{align}
& \text{Volume of the Cone }\left( V \right)=\frac{1}{3}\times \left( 45\pi \right)\text{y}{{\text{d}}^{3}} \\
& =15\pi \text{ y}{{\text{d}}^{3}} \\
& =47\text{y}{{\text{d}}^{3}}
\end{align}\]