Question 31 Find the volume of the solid generated by...

Question 31 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y = -3x + 6, y = 3x, x = 0 Selected Answer: 6? Answers: 9? 54? 18? 6?

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00:01 All right, we want to send the region bounded by 6y minus y squared, x equals 6y minus y squared, and the y axis about the x axis.

00:11 So x equals y squared is a sideways parabola.

00:19 And so this is a sideways parabola going backwards.

00:24 I'm going to factor out of y here.

00:26 We'll get 6 minus y.

00:29 So when x is 0, y is 0 and 6.

00:41 What should i do now? well, what if i took the derivative to find the vertex, x prime equals 6 minus 2y, so y equals 3, and if y equals 3, x equals 18 minus 9, which is 9.

01:06 So 1, 2, oh, i'm way over here at 9.

01:11 Pretend like this is it.

01:13 9 .3.

01:17 All right.

01:17 So there's the parabola.

01:19 Oops.

01:21 And then the y -axis right here.

01:24 So it's this shape here.

01:27 We're going to send it around the x -axis.

01:32 All right.

01:32 Let's assume.

01:34 I'm going to assume you know how to do shells.

01:36 If you don't, post it again and somebody and say use disk method.

01:42 All right.

01:44 So do you use shells? you've got to cut it parallel to the axis.

01:47 Of rotation.

01:50 So that little sliver will go around...

Question

Question 31 Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y = -3x + 6, y = 3x, x = 0 Selected Answer: 6? Answers: 9? 54? 18? 6?

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