Answer:
[tex](\pi 4^2 (9))-(\pi 2^2 (9))[/tex]
and
[tex]339.292 cm^3[/tex]
Step-by-step explanation:
This question is simple once you break it down.
Let's concentrate on the outer cylinder.
First, find the volume of the outer cylinder.
The volume of a cylinder is expressed as: [tex]V = \pi r^2 h[/tex]
Gathering information from the diagram..
d = 8 cm
h = 9 cm
You can get the radius from the diameter by just dividing the diameter by 2.
[tex]r = \frac{8}{2}=4[/tex]
r = 4
Plug everything into the volume equation.
[tex]V = \pi 4^2 (9)[/tex]
Don't solve just yet!
Now, find the volume of the inner cylinder.
Do the exact same thing as you did for the outer cylinder.
d = 4 cm
h = 9 cm
[tex]r = \frac{4}{2}=2[/tex]
r = 2
Plug everything into the volume equation..
[tex]V = \pi 2^2 (9)[/tex]
The question asks for an expression to represent the volume of the large cylinder after the cylindrical hole is removed. This means you need to subtract the volume of the cylindrical hole from the volume for the large cylinder.
Again, the volume for the large cylinder is [tex]V = \pi 4^2 (9)[/tex] and the volume for the cylindrical hole is [tex]V = \pi 2^2 (9)[/tex]
This means..
[tex](\pi 4^2 (9))-(\pi 2^2 (9))[/tex]
That is your answer to the first part of the question.
For the second part, just solve.
[tex](\pi 4^2 (9))-(\pi 2^2 (9))[/tex]
[tex](\pi*16*9)-(\pi*4*9)[/tex]
[tex](\pi*144)-(\pi*36)[/tex]
[tex]144\pi-36\pi[/tex]
[tex]108\pi[/tex]
[tex]339.292[/tex]
Don't forget the units.
[tex]339.292 cm^3[/tex]
Hope this helped you!
