How do I find the volume of a described solid using integration?

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Homework Help Overview

The discussion revolves around finding the volume of a solid using integration techniques. The original poster describes a solid and expresses confusion about how to set up the integral for volume calculation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to visualize the solid and suggests an initial integral setup. Some participants question how to relate the radius to the height and propose using a variable for the radius as a function of height.

Discussion Status

The conversation is progressing with participants providing hints and clarifications about the integration process. There is an indication that the original poster has made a breakthrough in understanding the problem.

Contextual Notes

Participants note that certain parameters such as r, R, and h are constants in the context of the problem, and there is a focus on defining the radius as a function of height for the integration.

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Homework Statement


I uploaded of a picture of the question so hopefully it comes up here.

Homework Equations





The Attempt at a Solution



OK! so i am SO confused on where to start.
I am imagining the solid flipped on its side with the x-axis going through its center.

So all i have is that the integral would be from 0 to h of (pi)(r)^2
Is this at all close?
Any hints would be greatly appreciated. :)
 

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That's a start but you have to relate r to h and then integrate over h.
 
r, R and h are given as constants in your diagram. Let's not integrate over any of them. Let y be the distance from the bottom of your solid. So y goes from 0 to h. Then your integral is the integral of (pi)(ρ(y))^2*dy for y from 0 to h. Where ρ(y) is the cross sectional radius of your solid at the height y. ρ(0)=R, ρ(h)=r. Can you figure out an expression for ρ(y) at a general height y?
 
I GOT IT !
thanks for the help dick :)
 

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