Answer:
[tex]The\ total\ volume\ is\ 32\pi\ inches^{3}.[/tex]
Step-by-step explanation:
Formula
[tex]Volume\ of\ a\ cylinder = \pi r^{2} h[/tex]
Where r is the radius and h is the height.
As given
A company designs its packaging so that it is a cylinder with a diameter of 4 inches and a height of 7 inches.
[tex]Radius (r) = \frac{Diameter}{2}[/tex]
[tex]Radius (r) = \frac{4}{2}[/tex]
Radius (r) = 2 inches
Put in the formula
[tex]Volume\ of\ a\ cylinder = \pi\times 2\times 2\times 7[/tex]
[tex]Volume\ of\ a\ cylinder =28 \pi[/tex]
Formula
[tex]Volume\ of\ a\ cone = \pi r^{2} \frac{h}{3}[/tex]
Where r is the radius and h is the height.
As given.
cone on top of the cylinder that has a diameter of 4 inches and a height of 3 inches.
[tex]Radius (r) = \frac{Diameter}{2}[/tex]
[tex]Radius (r) = \frac{4}{2}[/tex]
Radius (r) = 2 inches
Put in the formula
[tex]Volume\ of\ a\ cone = \pi\times 2\times 2\times \frac{3}{3}[/tex]
[tex]Volume\ of\ a\ cone = 4\pi[/tex]
Total area = volume of a cylinder + volume of a cone
[tex]Total\ volume= 28\pi+ 4\pi[/tex]
[tex]Total\ volume= 32pi\ inches^{3}[/tex]
[tex]Therefore\ the\ total\ volume\ is\ 32\pi\ inches^{3}.[/tex]
