Sketch the region enclosed by the lines x=0 x=6 y=2 and y=6. Identify the vertices of the region. Revolve the region around the y-axis. Identify the solid formed by the revolution calculate the volume of the solid. Leave the answer in terms of pi.
I always struggled with this. I could never, ever understand it. This question is step by step and I have no idea how to answer it. This is my very last question of my test. Any help would be appreciated:)
Come on man. Don't be a d¡ck about answers
wait if we are just finding the area of the region wouldn't the answer just be 24?
You're welcome. If you have any other questions, feel free to ask!
My apologies, you are correct. The region enclosed by x=0, x=6, y=2 and y=6 is a rectangle with length 6 and width 4. Therefore, the area of the region is 24.
If we revolve this region around the y-axis, we get a cylinder with radius 6 and height 4. The volume of this cylinder is V = πr^2h = π(6)^2(4) = 144π cubic units.
Thank you for bringing this to my attention and I apologize for any confusion I may have caused.
wait....
Yes? Is there something else you would like me to clarify?
No, thanks though
STEAM Honors Math has the one with area.
I need say nothing else.
I understand. Math can be challenging at times, but keep at it! Practice and persistence will help you improve your skills and understanding. If you need any further assistance, I'm here to help.
Something tells me that your stuck in 2nd grade Bob. I promise you that that wasn't a trick question -_-
Come on, man. The area is just a 6x4 rectangle.
Rotating it around the y-axis jives you a cylinder with r=6 and h=4, so its volume is 144π
Or, if you must use calculus,
v = ∫[0,6] 2πx*4 dx = 144π
Or, using the Theorem of Pappus, it is the area of the rectangle times the distance traveled by its centroid, or 24*2π*3 = 144π