help in finding volume

[morteza08]

cross section area of this body is a circle with radius R. and the cones at the ends are the same.. write down a procedure to calculate the volume based on h.
0<h<2R

 

[stapel]

You've posted this elsewhere as being a geometry exercise. Is this actually a problem from a calculus class?

Either way, please reply showing your thoughts and efforts so far. Thank you!

 

[morteza08]

You've posted this elsewhere as being a geometry exercise. Is this actually a problem from a calculus class?

Either way, please reply showing your thoughts and efforts so far. Thank you!

It can be a problem of geometry and calculus... We are calculating the volume of a body, so it can be geometric . and we are using integration and it relates to calculus...
I am uploading my works. but you can not understand them.. actually, I misunderstand the problem and I just find out the real problem...
suppose this is a water reservoir, and we fill it up to height h.... then calculate the volume of water based on h...

thank you..

 

[HallsofIvy]

I wouldn't call it a calculus problem, just an exercise in combining volume formulas.
You have a cylinder of radius R and height L- its volume is given by \(\displaystyle V= \pi R^2L\).
You also have two right cones of radius R and height d. The volume or such a cone is given by \(\displaystyle V= \frac{1}{3}\pi R^2 d\).

But the problem says "based on h". It isn't clear to me what part of the figure "h" is supposed to be. It looks, from the figure, that h is a part of the radius but what part?

 

[morteza08]

what is h

we are not to calculate the volume of the reservoir.We should calculate the volume of water and h is the height of water in the reservoir... it ranges from 0 to 2Rcalculate the volume of water with respect to h.

 

[stapel]

I wouldn't call it a calculus problem, just an exercise in combining volume formulas....

But the problem says "based on h". It isn't clear to me what part of the figure "h" is supposed to be.

That's where the calculus comes in. The "h" is the height of the fluid inside the tank, while the tank is lying on its side.

 

[Deleted member 4993]

cross section area of this body is a circle with radius R. and the cones at the ends are the same.. write down a procedure to calculate the volume based on h.
0<h<2RView attachment 4347

Now that we know what the problem is - What are your thoughts?

Where do you begin?

Please share your work with us ...

If you are stuck at the beginning tell us and we'll start with the definitions.

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