Cross-sectional volume question?  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Cross-sectional volume question?  TOPIC_SOLVED

Postby Thatguy73 on Wed Aug 18, 2010 2:07 am

So I would like to know if I am doing this correctly. Here's the question:

Solid B has a volume of 8(pi)

It also is a Pyramid with a square base and a height of 8. What is the length of the side (s) of the base of B?

The Cross-sectional area would be A(x)=s^2 And I would need to write s in terms of x to put it in the definite integral to find the volume.

Since the height of the pyramid 8, I can make the Vertex of it at (0,0) and then make the base centered at (8,0). So the cross-sectional areas would need to be summed up on the interval [0,8]. I can find the volume of the pyramid:





At the end of the base where x=8, the side (s) of the base would be 2y. So then something times x must give 2y

Therefore

Since k^2 is a constant:




Solving for k:



Since: Plug in x=8 and k.



Could someone tell if this method is correct? I just started learning this and it's kind of confusing.

Thanks
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Re: Cross-sectional volume question?

Postby Martingale on Wed Aug 18, 2010 3:51 am

Thatguy73 wrote:So I would like to know if I am doing this correctly. Here's the question:

Solid B has a volume of 8(pi)

It also is a Pyramid with a square base and a height of 8. What is the length of the side (s) of the base of B?

The Cross-sectional area would be A(x)=s^2 And I would need to write s in terms of x to put it in the definite integral to find the volume.

Since the height of the pyramid 8, I can make the Vertex of it at (0,0) and then make the base centered at (8,0). So the cross-sectional areas would need to be summed up on the interval [0,8]. I can find the volume of the pyramid:





At the end of the base where x=8, the side (s) of the base would be 2y. So then something times x must give 2y

Therefore

Since k^2 is a constant:




Solving for k:



Since: Plug in x=8 and k.



Could someone tell if this method is correct? I just started learning this and it's kind of confusing.

Thanks


your answer is correct (if you allow for rounding)
the exact answer is
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