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volumes of revolution

how would I do Q3ii)

this is what I did

integral of pi(25-x²)
=pi[25x-(1/3)x³] with limits 3 and -3
=pi((75-9)-(-75+9))
=132pi

Have I done something wrong and what do I do next?
IMAG0042.jpg459.1KB
Original post by helpme456
...


As the question says, you need to consider the shaded area as the difference between two areas; and then two volumes.

You've found the volume if you rotate the curve about the x-axis.

Now you need to find the volume of that interior cylinder, and subtract it from the first.

This will give you the required answer.
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helpme456
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Original post by ghostwalker
As the question says, you need to consider the shaded area as the difference between two areas; and then two volumes.

You've found the volume if you rotate the curve about the x-axis.

Now you need to find the volume of that interior cylinder, and subtract it from the first.

This will give you the required answer.


how can I find the interior cylinder volume?
(edited 11 years ago)
Original post by helpme456
how can I find the interior cylinder volume?


Refering to your diagram - don't forget the x-axis is the centre of rotation.

Radius is ...?

And height is ...?

And formula for volume of a cylinder is...?
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helpme456
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Original post by ghostwalker
Refering to your diagram - don't forget the x-axis is the centre of rotation.

Radius is ...?

And height is ...?

And formula for volume of a cylinder is...?


isnt the interior a rectangle though so its volume would be a cuboid not a cylinder
(edited 11 years ago)
Original post by helpme456
I thought that another volume of rev had to be done, didnt think of using the equation of volume

r²hpi
=36pi

132pi-2(36pi) = 60pi

STILL not right, what have I done wrong this time


What's your radius and what's your height? Don't forget it's r^2 in there.
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Original post by ghostwalker
What's your radius and what's your height? Don't forget it's r^2 in there.


if its the interior we are finding then will the radius be 3 and the height 8

9*pi*8 = 72pi
pi(132-72) = 60pi

the answer should be 36pi

also, why is the volume of cylinder being used, isnt the interior a rectangle?
Original post by helpme456
if its the interior we are finding then will the radius be 3 and the height 8

9*pi*8 = 72pi
pi(132-72) = 60pi

the answer should be 36pi

also, why is the volume of cylinder being used, isnt the interior a rectangle?


It's a rectangle rotated about the x-axis, giving a cylinder.

The radius is 4, the y value of the straight line at the base of the segment of the circle.

And the height is 3-(-3).
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Original post by ghostwalker
It's a rectangle rotated about the x-axis, giving a cylinder.

The radius is 4, the y value of the straight line at the base of the segment of the circle.

And the height is 3-(-3).


How am I supposed to know if the the x part is the radius or the height
Original post by helpme456
How am I supposed to know if the the x part is the radius or the height


By the fact that the rotation is about the x-axis, as the question says. So the x-axis is the centre, and any line perpendicular to it will be a radius.
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Original post by ghostwalker
By the fact that the rotation is about the x-axis, as the question says. So the x-axis is the centre, and any line perpendicular to it will be a radius.


After visualising I can see what you mean. Thanks for sticking at it to make me understand, really appreciated
Original post by helpme456
After visualising I can see what you mean. Thanks for sticking at it to make me understand, really appreciated


Np. Visualising is a useful technique with some of this "stuff". If only it worked with algebra.

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