Step 1
State the formula for the volume of a cone.
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Where;
[tex]\begin{gathered} r=3\text{ f}t \\ h=5ft \end{gathered}[/tex]
Step 2
Find the volume of the cone in the figure.
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times3^2\times5 \\ V=\frac{\pi\times9\times5}{3} \\ V=15\pi ft^3 \end{gathered}[/tex]
Step 3
State the formula for the volume of a cylinder
[tex]V=\pi r^2h[/tex]
where;
[tex]\begin{gathered} r=3ft \\ h=6ft \end{gathered}[/tex]
Step 4
Find the volume of the cylinder.
[tex]\begin{gathered} V=\pi\times3^2\times6 \\ V=\pi\times9\times6 \\ V=54\pi ft^3 \end{gathered}[/tex]
The total volume of the figure is, therefore;
[tex]\begin{gathered} V=\text{volume of cone + volume of cylinder} \\ V=15\pi+54\pi \\ V=69\pi ft^3 \end{gathered}[/tex]
The total volume of the figure in terms of π=69π cubic feet
Answer;69π cubic feet
