When to use the disk method?

If you have a function y=f(x) and you rotate it about the x axis , you should use disk (or ring, same thing in my mind). If you rotate y=f(x) about the y axis, you should use shell. Of course, you can always use both methods if you can find the inverse of the function.

How to know whether to use the disk or washer method?

You can always use either, the difference is that the washer method takes the cross-section of your final shape, then rotates it, while the disk method subtracts the entire volume of the shape enclosed by g(x) from the shape enclosed by f(x) .

What is the shell method of finding volume?

Shell Method is used to find the volume by decomposing a solid of revolution into cylindrical shells . We slice the solid parallel to the axis of revolution that creates the shells. The volume of the cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall.

How to find the volume of a disk?

Volume of a Disk A circle is a two-dimensional figure, while a disk is a three-dimensional cylinder with a small height measurement. The volume of a disk is typically found using the same formula as a cylinder: V = π r 2 h .

What is the shell method in chemistry?

Shell Model of the Atom The shell which is closest to the nucleus is the first shell . The sequence in which the electrons occupy the shell is given as: 2, 8, 18, 32, 50, 72, 98. The atomic shell model also helps in understanding the chemical properties of the atoms.

Is shell method on AP Calc BC?

No need to fret - the Shell Method isn't specifically tested on the AP Calculus AB exam. The AB exam covers topics in differential and integral calculus, but the Shell Method, which is a technique for finding the volumes of solids of revolution, is actually part of the BC curriculum .

Why is the disk method a special case of the general slicing method?

We can observe that the disk method is a special case of the general slicing method by comparing their formulas . The disk method formula is simply the general slicing method formula with the area A(x) or A(y) being replaced by the area of a circular disk, that is, πR^2.

What is the formula for the shell method?

The Shell Method Formula The general shell method formula is V = ∫ a b 2 π r h ( r ) d r where r is the radius of the cylindrical shell, h(r) is a function of the shell's height based on the radius, and dr is the change in the radius.

Decide whether it is more convenient to use the disk method or the shell method to find the volume of the solid of revolution. Explain your reasoning. (Do not find the volume.) y=4-e^x Graph can't copy

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Decide whether it is more convenient to use the disk method or the shell method to find the volume of the solid of revolution. Explain your reasoning. (Do not find the volume.) y=4-e^x Graph can't copy | Numerade (2024)

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When to use the disk method? ›