Finding volume of a solid about a vertical lineHow can I calculate the volume of...

makaunawal5

makaunawal5

Answered

2022-07-23

Finding volume of a solid about a vertical line
How can I calculate the volume of the solid generated by rotating the region bounded by
y = x 2 6 x + 10
and y = x 2 + 4 x + 2.
About the line x = 4

Answer & Explanation

Tristan Pittman

Tristan Pittman

Expert

2022-07-24Added 14 answers

Step 1
Use cylindrical shells.
Your representative rectangle would be vertical, and its width is dx and its height is
x 2 + 4 x + 2 ( x 2 6 x + 10 ) = 2 x 2 + 10 x 8
Step 2
Now, construct your integral:
2 π 1 4 p ( x ) h ( x ) d x
p ( x ) = 4 x since you're rotating around the line x = 4.
2 π 1 4 ( 4 x ) ( 2 x 2 + 10 x 8 ) d x = 27 π 2
comment if you need more help.

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