Find the volume of a solid generated by the region bounded above by the line y=16, below by the curve y=16-x^2 and on the right by the line x=4.

I think I can draw the basic shape, but I can't figure out how to set up the integral. The correct answer is 1025pi/5

Question

Find the volume of a solid generated by the region bounded above by the line y=16, below by the curve y=16-x^2 and on the right by the line x=4.

I think I can draw the basic shape, but I can't figure out how to set up the integral. The correct answer is 1025pi/5

theoreo · Answer

|dw:1401340475447:dw| I think this is what the drawing should look like. Sorry I kinda suck with art.

anonymous · Answer

your sketch is incorrect. What does y = 16 - x^2 look like?

anonymous · Answer

you mean on the left of x = 4?

theoreo · Answer

y=16-x^2 looks like the curve below y=16. I reflected it over y=16 to simulate the revolution since that's how I was taught.  Yes, the region to the left of x=4.

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Here's a drawing of just the region.

anonymous · Answer

disk method

theoreo · Answer

Yes, that's what I'm trying. But every equation I've tried so far for the radius of the disk is wrong.

anonymous · Answer

well what is the radius?

anonymous · Answer

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