Volume problem

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• Nov 21st 2010, 08:57 PM
nhunhu9
Volume problem
A rectangle with vertices (0,0), (4,0), (4,6) and (0,6) is revolved about the x-axis to create a cylinder. What is the volume of this cylinder?
A. 32pi
B. 96pi
C. 144pi
D.288pi
E.NOTA (none of these above)

I'm thingking of NOTA. But it confuses me at the part where it says "revolved about the x-axis", i don't know if the way I understand it is correct, because if it's not then I definitely solved it wrong :P
• Nov 21st 2010, 09:06 PM
FernandoRevilla
The solution is:

$\displaystyle V=\pi r^2h=\pi \cdot 6^2\cdot 4=144\pi$.

Regards.

Fernando Revilla
• Nov 21st 2010, 09:07 PM
pickslides
I like this answer

Quote:

Originally Posted by nhunhu9
C. 144pi

Taking a rectangle and revolving it around the x-axis certainly creates a cylinder.

Step 1. Draw the rectangle

Step 2. Draw the cylinder

Then using $\displaystyle V = \pi r^2h$ with $\displaystyle r=6, h = 4 \implies V = \pi\times 6^2\times 4 = 144\pi$
• Nov 22nd 2010, 06:19 AM
nhunhu9
Thank you. I have another question, it sounds silly , but how to you know the radius is 6? I picture how a rectangle revolves around the x axis, and 6 looks like the circumference to me. Can you please explain?