Question

how to find the volume of a glass with the help of integration and with the use of ruler? please help me

Answer 1

A drawing, perhaps?

Answer 2

suppose I have a base curve and I rotate it along y-axis and it makes a glass.... then the vloume of that glass would be whaT???

Answer 3

Insufficient defintion. Still needs a better description.

For starters, if you've a curve, and you spin it around an axis, you will get an area, not a volume.

Answer 4

okey then as u are saying,,,tell me how to calculate the area with integration ...what will be the equation of that curve and the limits?

Answer 5

I recommend you read up on Pappus' Theorem. Find an effective centroid and spin away. It woudl help a lot if we had a clue what you were trying to do.

Answer 6

tkhunny, if you spin a curve around an axis, it forms something which you can calculate the volume of. you're thinking of a surface integral. but, the surface is the outer part of a figure that has volume.

Answer 7

http://en.wikipedia.org/wiki/Shell_integration

Answer 8

@slaaibak That is incorrect. Spinning a curve produces an area. Spinning an area under a curve, not that produces a volume.

Answer 9

tk - I agree, but that's what he is trying to say.

Answer 10

Fair enough. Do you think I've made enough fuss about it that the OP will now say what is meant? "-)

Answer 11

haha, we can only hope.

Answer 12

Well, u guyz are saying right but could u guyz plz give me an example solved to find the volume ....

Answer 13

I have made an attempt to find the volume ... and i use the equation of the base curve and the limits as radius of the base of the glass along x-axis.

Answer 14

Typically, using "Shells", we have:

Given f(x) defned on a region [a,b] with 0 <= a < b
And, for the sake of simplicity, f(x) >= 0 on [a,b]

\(\large 2\pi\int\limits_{a}^{b} x\cdot f(x)\;dx\)

If we use "Shells", we don't have to worry about the concavity of the shape.

Answer 15

Useful approximations can be made by measuring 'x' and relating it to f(x) for various widths and locations that capture the interesting parts of the curve.

Notice, if f(x) = 1, a constant of height 1 on [0,2], we have: \(2\pi\int\limits_{0}^{2}x\cdot 1\;dx = 2\pi\cdot \dfrac{2^{2}}{2} = 4\pi\), which is consistent with the volume of a right circular cone with radius 2 and height = 1.

Answer 16

can I do like that ? and then from these two points I can caluculate the equation f(x)... and then integrate it with using limits 0-5 ...guide me If I am wrong?