We have to find the volume of the cone, knowing the height of the cone (h=11 ft) and the radius of the base of the cone (r=7 ft).
The volume of a cone can be expressed as:
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Then, we can replace the values and calculate:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\pi\cdot7^2\cdot11 \\ V=\frac{1}{3}\pi\cdot49\cdot11 \\ V=\frac{539\pi}{3} \\ V\approx564.44 \end{gathered}[/tex]
The volume of the cone is approximately 564.44 ft^3.
For the sphere, we know the radius (r=22 yd).
The expression for the volume of a sphere is:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\pi\cdot22^3 \\ V=\frac{4}{3}\pi\cdot10648 \\ V=\frac{42592\pi}{3} \\ V\approx44602.24 \end{gathered}[/tex]
The volume of the sphere is approximately 44602.24 yd^3.
Answer:
Volume cone = 564.44 ft^3
Volume sphere = 44602.24 yd^3
