Thread: Finding the volume of the graph

1. Finding the volume of the graph

I'm supposed to find the volume of a graph. The equation of the graph is y=5-2cos(2x). The domain is from 0 to 3 $pi$/4. I have tried a million different ways, using integrals to figure this out, unfortunately, every single answer I get is wrong. I've tried u substitution as well as a few other methods, but I do not get a consistent area. I also don't understand how to get the volume from there, especially since if you rotate it, the radius wouldn't be constant.

a) 10pi+20.25pi^2
b).5pi^2
c).25
d)1/9
e)8pi + 21pi^2

- NothingButSmiles

2. Re: Finding the volume of the graph

Originally Posted by NothingButSmiles
I'm supposed to find the volume of a graph. The equation of the graph is y=5-2cos(2x). The domain is from 0 to 3 $pi$/4. I have tried a million different ways, using integrals to figure this out, unfortunately, every single answer I get is wrong. I've tried u substitution as well as a few other methods, but I do not get a consistent area. I also don't understand how to get the volume from there, especially since if you rotate it, the radius wouldn't be constant.

a) 10pi+20.25pi^2
b).5pi^2
c).25
d)1/9
e)8pi + 21pi^2

- NothingButSmiles
What do you mean 'Volume' ....? Do you mean the volume of a solid of revolution? Around what axis? Please post the whole question so that all informtaion is given.

3. Re: Finding the volume of the graph

Originally Posted by mr fantastic
What do you mean 'Volume' ....? Do you mean the volume of a solid of revolution? Around what axis? Please post the whole question so that all informtaion is given.
My paper says: Calculate the volume of the solid formed when the shaded region is rotated through 2pi radians about the x-axis.

Then it gives a graph of y = 5 - 2 cos (2x) with a domain of 0 to 3pi/4

4. Re: Finding the volume of the graph

Originally Posted by NothingButSmiles
My paper says: Calculate the volume of the solid formed when the shaded region is rotated through 2pi radians about the x-axis.

Then it gives a graph of y = 5 - 2 cos (2x) with a domain of 0 to 3pi/4
Can you write down the integral you are required to solve?

5. Re: Finding the volume of the graph

Originally Posted by mr fantastic
Can you write down the integral you are required to solve?
it doesn't say to use an integral, just to find the volume... I just used an itegral because that was what i thought I was supposeed to do

6. Re: Finding the volume of the graph

Can you describe the "shaded area"?

7. Re: Finding the volume of the graph

The correct answer is a). When the graph is rotated around the x axis it generates a volume. If you slice this volume with a blade perpendicular to the x axis and make a very thin slice, the slice is a disk whose radius is y or (5-2cos(2x)) the volume of the disk is y^2*pi *dx, where dx is the thickness of the disk. Now integrate this differential volume from 0 to 3pi/4, which gives you the whole volume. The result is: 10pi+20.25pi^2.

8. Re: Finding the volume of the graph

Originally Posted by NothingButSmiles
it doesn't say to use an integral, just to find the volume... I just used an itegral because that was what i thought I was supposeed to do
Have you been taught the application of integration to calculating the 'volume of a solid of revolution'? If not, I'm not sure why you would be set the question.

9. Re: Finding the volume of the graph

This may help a little better,