# Math Help - volume of revolution

1. ## volume of revolution

a drinking glass has the shape of a truncated cone. if the internal radii of the base and the top are 3cm and 4cm respectively and the depth is 10cm. if the glass is filled with water to a depth of 5cm, find the volume of the water

i found out that the equation of the line is x=4-(y/10)
and then using the volume formula between y=5 and y=0 i integrated it and worked it out to be 845pi/12 BUT the answer says the volume is 635pi/12 can anyone tell me where i went wrong?
thankyou !!

2. Your attempted working is incredibly vague but I shall take a shot at this.

First of all, judging by your equation, I believe you are using volumes of solids of revolution using circular discs, which uses the formula $V = \pi \int x^2 \,dy$ for revolutions about the y axis.

However, your equation is incorrect if you are to integrate between y = 0 to y = 5.

This is because you turned the cup up-side down with that equation. Integrating between y = 0 and 5 gives you the empty volume of the glass, not the volume of water.

To find the volume of water, either integrate between y = 5 to 10 with your equation, or flip the cup so it's base of 3 cm lies on the x axis. The equation for this is $y = 10x - 30 \Rightarrow x = \frac{y}{10} + 3$

3. Originally Posted by flyinhigh123
a drinking glass has the shape of a truncated cone. if the internal radii of the base and the top are 3cm and 4cm respectively and the depth is 10cm. if the glass is filled with water to a depth of 5cm, find the volume of the water

i found out that the equation of the line is x=4-(y/10)
and then using the volume formula between y=5 and y=0 i integrated it and worked it out to be 845pi/12 BUT the answer says the volume is 635pi/12 can anyone tell me where i went wrong?
thankyou !!

This question was already asked and answered, and who knows what did you do: I gave you the points (0,3) , (10,4) so that you'll see the line joining them as the side line between the glass's bottom and its top, and this line's eq. is simply $y-3=\frac{1}{10}x=\frac{x}{10}+3$.

Apparently you wanted to revolve the line around the y-axis, and I've no idea why, and you tried to express the line's eq. as a function of y instead of x, but then you'd get $x=10(y-3)$ and not what you wrote.

If you now revolve the above line between x = 0 and x = 5 then you get the water's volume in the glass, and for this you need to do the VERY SIMPLE integral $\pi \int\limits_{0}^5\left(\frac{x}{10}+3\right)^2dx$ , and then you get exactly $\frac{635\pi}{12}$

Tonio

4. Hey, ease up bro. Your claim to have "no idea why" someone did what they did, specific criticism and declaration that the integral is "VERY SIMPLE" are not really that constructive.

$
y-3=\frac{1}{10}x=\frac{x}{10}+3
$

isn't entirely correct (to be frank, it's mathematically wrong). Splitting it into 'y-3=' and then 'y=' might make your intentions more clear. Take a look at your audience and try to suit your replies to other people, without expressing your opinion of their abilities.

5. Originally Posted by chug1
Hey, ease up bro. Your claim to have "no idea why" someone did what they did, specific criticism and declaration that the integral is "VERY SIMPLE" are not really that constructive.

$
y-3=\frac{1}{10}x=\frac{x}{10}+3
$

isn't entirely correct (to be frank, it's mathematically wrong). Splitting it into 'y-3=' and then 'y=' might make your intentions more clear. Take a look at your audience and try to suit your replies to other people, without expressing your opinion of their abilities.
Some points to clear out, more for the general audience than specifically for this guy Chug1:

First: I am not, thanx goodness, your bro

Second: Of course I'm expressing criticism: I did answer this very question yesterday and got thanked for it and, instead of continuing the thread there and ask for further clarifications, the OP chose to open a new one, which is seen as not so nice a thing to do, to say the least, in most public forums; but EVEN then he took part of what was said in that answer of mine and made a mess out of it. My point stressing this out was to call his attention to this.

(3) My simple equation is indeed simple (an equation of a straight line in the xy-plane: 8-th grade mathematics at most. As simple as you can expect for someone taking integral calculus) and even more interresting, it is correct, in spite of the typo that happened there and which every serious 1st year college student can correct: it should have, of course, been

$y-3=\frac{1}{10}x\Longrightarrow y=\frac{x}{10}+3$

(4) It is unpolite, rude and frankly annoying to have somone butting into a thread of which he doesn't know the background, and even worse: to butt in in a bratty, whinning attitude, and even worse: you did not apport anything interesting from a mathematical point of view, unless pointing out trivial typos counts for you as mathematical contribution.

College and university studies in math are for serious, intelligent people, and being over-sensitive can cut somebody's opportunities short to succeed at them. Sometimes one needs a reprimand (and the above was a rather mild one) to wake up and buckle down. Hopefully this will work for you as well.

Tonio

6. My genuine apologies tonio.
I didn't realise the history of this question, though I see now an indicator to it in your first post. Better observance on my part should have shown to me this source of frustration.

From your statistics I can see an average of (at least) 5 thanks and 15 posts per day. My initial judgement of your character and forum contribution doesn't really fit with this, and again if I'd taken the time to look I might have acted with a bit more respect.

I can't really offer an excuse, like stress or a bad day, so I will just say that I, ultimately, value your comments as self improvement (medicine always tastes bad) and will think a bit more next time.

Glen

7. Originally Posted by chug1
My genuine apologies tonio.
I didn't realise the history of this question, though I see now an indicator to it in your first post. Better observance on my part should have shown to me this source of frustration.

From your statistics I can see an average of (at least) 5 thanks and 15 posts per day. My initial judgement of your character and forum contribution doesn't really fit with this, and again if I'd taken the time to look I might have acted with a bit more respect.

I can't really offer an excuse, like stress or a bad day, so I will just say that I, ultimately, value your comments as self improvement (medicine always tastes bad) and will think a bit more next time.

Glen

I really thank you for your last message and this already is behind us.

Tonio

8. Originally Posted by tonio
I really thank you for your last message and this already is behind us.

Tonio
The OP can do the right thing and ask in the original thread (http://www.mathhelpforum.com/math-he...tegration.html) for further clarification (if needed) of matters discussed in this thread.

Aside: This thread highlights one of the many good reasons why there are forum rules and why following them is strictly enforced.