Answer:
Exact volume: 36.75π yd³
Rounded volume: 115.5 yd³ (nearest tenth)
Step-by-step explanation:
To find the volume of a cone, we can use the following formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Volume of a Cone}}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$V$ is the volume.}\\\phantom{ww}\bullet\;\textsf{$r$ is the radius of the circular base.}\\\phantom{ww}\bullet\;\textsf{$h$ is the height.}\end{array}}[/tex]
The circular base of the given cone has a diameter of 7 yd. Since the radius of a circle is half its diameter, then r = 3.5 yd.
Substitute r = 3.5 yd and h = 9 yd into the formula and solve for V:
[tex]V=\dfrac{1}{3} \cdot \pi \cdot 3.5^2 \cdot 9\\\\\\\\V=\dfrac{1}{3} \cdot \pi \cdot 12.25 \cdot 9\\\\\\\\V=\dfrac{1}{3} \cdot \pi \cdot 110.25\\\\\\\\V=36.75 \pi \\\\\\ V=115.45353001...\\\\\\V=115.5\; \sf \sf yd^3\;(nearest\;tenth)[/tex]
Therefore, the exact volume of the cone is 36.75π cubic yards, which is approximately 115.5 cubic yards, rounded to the nearest tenth.
