Question

Volume of revolution.
How would I find the volume of revolution for a space between two curves y=-x^2 +9 y=-x from x=0 to x=2

Answer 1

graph it first

Answer 2

Already did, i would apply the formula but the space between the two curves is crossing the x-axis. What if the question asked for the vol of rev about the x-axis? How would i do that?

Answer 3

Hey, volume or area?

Answer 4

if it is area, then easy
but if it is volume, then you need a rotation axis.

Answer 5

First off, this is a hypothetical question i made up. And i want to find the volume of rev

Answer 6

What?? you made it up?? wow...
@IrishBoy123

Answer 7

Usually, when we are asked to do a volume of rev in class, the space between the two curves are always in the 1st quadrant. I want to know if the procedure would change if the space were to be in the the 1st and the 4th simultaneously.

Answer 8

should i just shift both functions upwards to avoid complications?

Answer 9

you can only revolve this around y-axis whilst retaining any sense to the whole thing, ie whilst getting what might be described as a volume

as @Loser66 said, you should draw it. that's the best advice by far. i can see only arrows on what you posted. not the curves and their intersections.

when you see the actual **area** that you are revolving to form a **volume**, i am sure you will see the conundrum.

you could revolve your area about any axis you want and get a mathematical answer but it wouldn't be a volume, would it?!