Answer:
[tex]V=39\pi\ cm^3[/tex]
Step-by-step explanation:
we know that
The volume of a cone is given by the formula
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
where
r is the radius of the circular base of cone
h is the height of the cone
step 1
Find the volume of the top cone
we have
[tex]r=3\ cm\\h=5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}\pi (3)^{2} (5)[/tex]
[tex]V=15\pi\ cm^3[/tex]
step 2
Find the volume of the bottom cone
we have
[tex]r=3\ cm\\h=8\ cm[/tex]
substitute
[tex]V=\frac{1}{3}\pi (3)^{2} (8)[/tex]
[tex]V=24\pi\ cm^3[/tex]
step 3
Find the exact volume of the composite figure
Adds the volume of the top cone plus the volume of the bottom cone
[tex]V=(15\pi+24\pi)=39\pi\ cm^3[/tex]
