Hello kazafire93. Welcome to PF !kazafire93 said:Homework Statement
Hi, I'm having a tremendous amount of difficulty with finding the radii in problems using cylindrical shells.
Here's the question: find the volume of the solid found by rotating the region bounded by the given curves:
x = y2+1, x = 2, about y = -2
I got 2 - (y2+1) for the height, which I know is correct. For the radius, though, I got 1 + y...which is incorrect. Can anyone explain how to get the right answer? Thanks!
The formula for finding the radius of a cylindrical shell is r = h/2π, where h represents the height of the cylindrical shell and π is the mathematical constant pi.
The radius of a cylindrical shell is directly proportional to its volume. This means that as the radius increases, the volume of the cylindrical shell also increases.
No, the radius of a cylindrical shell cannot be negative. The radius represents the distance from the center of the cylinder to its outer surface, and distance cannot be negative.
The formula for calculating the surface area of a cylindrical shell is A = 2πrh + 2πr², where r is the radius and h is the height of the cylindrical shell.
Yes, the radius of a cylindrical shell can be larger than its height. This is often the case with objects such as cans or tubes, where the radius is significantly larger than the height.