A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the yaxis, and the line y = 3 about the yaxis.
anonymous
 one year ago
Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the yaxis, and the line y = 3 about the yaxis.

This Question is Closed

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Ooo solids o revolution :) These are so fun

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0eh, I'd rather play a game of tag

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3dw:1444438841566:dwOk so you can see the region that we're dealing with.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3dw:1444439029610:dwWe're integrating `from x=0` and `to x= the intersection of these two curves`.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm y=3,\qquad\qquad y=1+\sqrt x\]\[\large\rm 3=1+\sqrt x\]So what is our upper bound on x?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm V=\int\limits_0^4 dv\]Ok that takes care of that. Now let's cut a little slice into that region, and see if we can come up with an equation for the volumen of the shape that is spun around.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3dw:1444439321599:dwWe're going to cut a little slice, we'll say that it has "thickness" dx

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3dw:1444439387037:dwLooks like we get a cylindrical shell, ya? We have some information we need to figure out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So we need to find r and h?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Volume of a cylindrical shell is \(\large\rm v=(Circumference)(height)(Thickness)\) Good, yes. We already know the thickness,\[\large\rm dv=(Circumference)(height)(dx)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3dw:1444439652366:dwFor this particular problem, r is the easy one, h is going to be a little more difficult to figure out.