# Math

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:)

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1. 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

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