Answer:
574.82 cubic yards
Step-by-step explanation:
The diameter of the cone =14 yards
The angle between the height and slant height measures 32 degrees.
First, we determine the height of the cone using trigonometry.
In Right Triangle AOB,
[tex]Tan 32=\dfrac{7}{|AO|} \\|AO|*Tan 32 =7\\$Height of the Cone, $|AO|=\dfrac{7}{Tan 32} =11.2023 \:yards[/tex]
[tex]\text{Volume of a Cone=}\dfrac{1}{3}\pi r^2h\\Volume =\dfrac{1}{3}\pi*7^2*11.2023\\=574.82$ cubic yards[/tex]
The volume is about 575 cubic yards.
