calculating volume of a solid

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Erin0702

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Calculate the volume of the solid bounded above by the surface in #1, below by the xy-plane, and laterally by the planes y=0, y=4, and x=3 by using elementary geometry.

Do NOT use a Riemann sum.

The surface in #1 is z=x^2.

I know this should be basic but I'm not sure how to solve it other than by using iterated integrals which is what it asks for in the next part.

Any help would be great! :)
 
Since x=3, what does z equal?.

You now have x, y and z.

That's all you need for volume.
 
Erin0702 said:
Calculate the volume of the solid bounded above by the surface in #1, below by the xy-plane, and laterally by the planes y=0, y=4, and x=3 by using elementary geometry.

Do NOT use a Riemann sum.

The surface in #1 is z=x^2.

I know this should be basic but I'm not sure how to solve it other than by using iterated integrals which is what it asks for in the next part.

Any help would be great! :)
Click to expand...
I think you're supposed to use that the area under a parabola is 2/3 base * height.

parabol.gif


But you'll have to turn this upside down and use the non-shaded area. Then turn that area into a volume by mutiplying by the length along the y-axis.
 
Sorry...one more quick question about this one...which y value do I use? I've been given y=0 and y=4?

Thanks!
 
Erin0702 said:
Sorry...one more quick question about this one...which y value do I use? I've been given y=0 and y=4?

Thanks!
Click to expand...
The length is the difference between the endpoints.
 
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