Find the volume of the solid obtained by rotating the region-2

In summary, the task at hand is to find the volume of a solid formed by rotating the region bounded by the curves y=sqrt(25-x^2), y=0, x=2, and x=4 around the x-axis. A graph has been provided and assistance is requested in finding the solution using disks.
  • #1
phillyolly
157
0

Homework Statement


Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. About x axis.

y=sqrt(25-x2)
y=0
x=2
x=4

Homework Equations





The Attempt at a Solution


I drew a graph, region and solid. Please help me out with the disk.
Jump start for any solution, please?
 

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  • #2
I posted this in your other thread, here's the link: https://www.physicsforums.com/showthread.php?t=418382"

This figure should give you some intuition on visualizing the disks.

I don't really understand where your confusion lies, so if there is any please specify where and why.
 
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What is the definition of volume?

Volume is the amount of space occupied by a three-dimensional object.

How do you find the volume of a solid obtained by rotating a region?

The volume of a solid obtained by rotating a region can be found using the formula V = π∫(f(x))^2dx, where f(x) is the function representing the boundary of the region and the integral is taken over the interval of rotation.

Can the region be rotated around any axis?

Yes, the region can be rotated around any axis as long as the resulting solid is still completely contained within the boundaries of the original region.

What is the difference between a solid obtained by rotating a region and a solid with a known formula?

A solid obtained by rotating a region has a varying cross-sectional area, while a solid with a known formula has a constant cross-sectional area.

How is the volume affected by the shape of the region?

The volume is affected by the shape of the region because the cross-sectional area will change depending on the shape of the region. A larger cross-sectional area will result in a larger volume and vice versa.

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