Hollow Cylinder Question

[ganjum2671]

A jar made of 1/4 inch thick glass has an inside radius of 3.5 inches and total height of 11.3 inches (including the bottom thickness of glass). What is the volume of the glass shell of the jar (in cubic inches)?

 

[topsquark]

Hint: It looks like you can find the volume of a cylinder of radius (3.5 + 0.25) in then remove a cylinder of radius 3.5 in...

-Dan

 

[ganjum2671]

Why wouldn't we do 0.5 (diameter of the outside portion) and add that with 3.5 (radius of the inside) to find the total radius of the entire thing?

 

[Dr.Peterson]

Because the radius of the outer circle starts at the center, goes to the inner circle's radius, and then adds the thickness of the glass only once.

The diameter is 0.5 more than the inner diameter, but this is the radius.

 

[topsquark]

Why wouldn't we do 0.5 (diameter of the outside portion) and add that with 3.5 (radius of the inside) to find the total radius of the entire thing?

I'm not quite sure what you are asking. If we had one cylinder, without the hollowed out part, we would have a cylinder of radius (3.5 + 0.25) in. Are you trying to confirm that?

-Dan

Edit: Doc caught it.

 

[Dr.Peterson]

You can use the following formula:-

Volume of Hollow Cylinder =π*h*(R^2-r^2)
where
h=height of cylinder
R=Outer radius
r=Inner radius

Note that this formula amounts to the same method topsquark recommended (which doesn't require memorizing a separate formula). But it doesn't deal with the bottom of the glass, which none of us have mentioned yet. It is actually for a pipe, not a hollow cylinder with a solid bottom.

What you actually need to do is either to apply this formula to the part above the base and add on the entire base (a cylinder with height 0.25 in), or subtract from the volume of a cylinder with radius 3.75 and height 11.3, an inner cylinder with radius 3.5 and height 11.05. Do you see that?

 

[MarkFL]

Note that this formula amounts to the same method topsquark recommended (which doesn't require memorizing a separate formula). But it doesn't deal with the bottom of the glass, which none of us have mentioned yet. It is actually for a pipe, not a hollow cylinder with a solid bottom.

What you actually need to do is either to apply this formula to the part above the base and add on the entire base (a cylinder with height 0.25 in), or subtract from the volume of a cylinder with radius 3.75 and height 11.3, an inner cylinder with radius 3.5 and height 11.05. Do you see that?

That user turned out to be a spammer, and was shown the door. Sorry they wasted your time.

 

[Dr.Peterson]

Actually, they called my attention to the fact that previous answers were incomplete. No waste.