Frustum Problem

[Kaitlyn25]

Problem:

Find the volume of the solid shown in the figure (frustum) if the radius of the upper circular top is r₁=2, the radius of the circular top at the bottom is r₂=6 and the height of the solid is h=8.

Solution:

I originally just googled how to do a frustum and it provided a formula to do them, which is fine, but I'm not sure that's what the teacher wants from us. We didn't have time to finish this example in class but I know how I'm doing it is not how the instructor started to do it in class. What does this problem actually call for? We're currently studying applications of integrals and I think the approach has something to do with integrating with one of the volume methods but, again, we didn't have time to cover it in class.



Is this correct? Also, I know this forum supports LaTex but, after googling it, I'm not any closer to knowing how to use it on the forums. Is there a specific way to utilize it or a place on the forums that discusses how to use it?

 

[Deleted member 4993]

Problem:

Find the volume of the solid shown in the figure (frustum) if the radius of the upper circular top is r₁=2, the radius of the circular top at the bottom is r₂=6 and the height of the solid is h=8.

Solution:

I originally just googled how to do a frustum and it provided a formula to do them, which is fine, but I'm not sure that's what the teacher wants from us. We didn't have time to finish this example in class but I know how I'm doing it is not how the instructor started to do it in class. What does this problem actually call for? We're currently studying applications of integrals and I think the approach has something to do with integrating with one of the volume methods but, again, we didn't have time to cover it in class.

View attachment 3251

Is this correct? Also, I know this forum supports LaTex but, after googling it, I'm not any closer to knowing how to use it on the forums. Is there a specific way to utilize it or a place on the forums that discusses how to use it?

Where is the figure?

Venturing a guess - without the picture - it wants you to use disks, parallel to the base and integrate over the height (perpendicular to the base).

 

[Kaitlyn25]

How to find f(x)

Thanks for responding.



The figure looks like the one above, with the only difference being that r=r₁ and R=r₂. I'm trying to visualize how to set the figure on a coordinate system. Would the height of the frustum run along the y-axis? Or would I have to lay it sideways so that the height runs along the x-axis?