Question

Does anyone have a fool proof method for solids of revolutions?

Answer 1

I just started Calc BC and I know it's coming, and I never really learned it and then it was it was on the AB exam and the teacher at my school was like "oh I don't like these questions" so I would really appreciate if anyone had any tips

Answer 2

I think you'd benefit most from addressing some actual problems. If you really want to practice finding solids of revolution, let's begin with some simple ones and progress to more complicated ones. Could you look ahead in your Calc BC study materials and choose a couple of problems involving solids of revolution to start with?

We'll also need to discuss three distinct methods for finding the volumes of solids of revolutions: disks, washers, shells.

Answer 3

I'm taking it online btw but I know the Calculus teacher at my school she helps me sometimes

Answer 4

Ok, I'll get my Princeton review book

Answer 5

OK, Find the volume of the solid that results when the region bounded by \[\Large \sqrt{9-x^2}\] and the x-axis is revolved around the x-axis

Answer 6

For a quick tip: Always draw the region of interest, then a sample shell/disk/washer. Determine the dimensions of one such shell/disk/washer, and find a general formula for the dimensions.

Answer 7

I like to think of it as a unified theory, rather than 2 or 3 different methods. I start with the fundamental premise that we are building a Right, Circular Cylinder.

\(Volume\;of\;Right\;Circular\;Cylinder: V = \pi r^{2}h\)

Note: \(\dfrac{dV}{dr} = 2\pi rh\) and this essentially defines the method of Shells.

\(V = 2\pi\int rh\;dr\)

Note: \(\dfrac{dV}{dh} = \pi r^{2}\) and this essentially defines the method of Disks.

\(V = \pi\int r^{2}\;dh\)