Answer:
The volume of the figure is equal to
[tex]\frac{1,225}{3}\pi\ ft^{3}[/tex] or [tex]408\frac{1}{3}\pi\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the composite figure is equal to the volume of a cone plus the volume of a cylinder
step 1
Fin the volume of a cone
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}H[/tex]
we have
[tex]r=7\ ft[/tex]
[tex]H=7\ ft[/tex]
substitute
[tex]V=\frac{1}{3}\pi (7^{2})(7)=\frac{343}{3}\pi\ ft^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=7\ ft[/tex]
[tex]h=6\ ft[/tex]
substitute
[tex]V=\pi (7^{2})(6)=294 \pi\ ft^{3}[/tex]
step 3
Find the volume of the figure
[tex]\frac{343}{3}\pi\ ft^{3}+294 \pi\ ft^{3}=\frac{1,225}{3}\pi\ ft^{3}[/tex]
Convert to mixed number
[tex]\frac{1,225}{3}\pi=\pi(\frac{1,224}{3}+\frac{1}{3})=408\frac{1}{3}\pi\ ft^{3}[/tex]
