Just a Simple* Math Question

**naut** · 05-01-2007, 08:35

*Simple is subjective

I've got this question for maths; but I can't get the equation which I have to integrate:

A drinking glass has a 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, find by integration, its capacity. If the glass is filled with water to a depth of 5cm, find the volume of the water.

Anybody know how to deduce an equation from this question?

**Sasaki Kojiro** · 05-01-2007, 08:42

Well I remember those problems were annoying if that's any consolation. Let's see, by integrating what you are doing is taking a really small slice with the area of the base, and than another and so on infinitely many times which gives you an approximation of the volume. Soooo I don't remember the details. You'll probably have 3 and 4 on the little squiggly thing.

**naut** · 05-01-2007, 08:49

Thanks for clearing that up for me.

**Sasaki Kojiro** · 05-01-2007, 08:52

Maybe c is 10?

Maybe you take the formula for volume of a cone and do some calculus thing to it and put 3 and 4 and 10 in their somehow? Man I don't remember calculus.

**Rodion Romanovich** · 05-01-2007, 09:14

Look at http://en.wikipedia.org/wiki/Volumes_of_revolution

**naut** · 05-01-2007, 09:19

Edit: I know how to integrate and find volume using integration.

**Vladimir** · 05-01-2007, 13:35

I took all the advanced courses I could in High School and I just realized that all of that information is just gone. What's pie?

**naut** · 05-01-2007, 13:45

Originally Posted by Vladimir

advanced courses I could in High School

Here in NSW we have the following levels of Math:

General - Basic, such as algebra, probability and statistics
2 Unit (which is what I'm doing) - Relatively difficult, the hardest stuff we do is application of calculus and the trigonometric functions
3 Unit (which I used to do) - Basically they do the 2 Unit course but very quickly and then do 5-6 more topics on top of that.
4 Unit - Simply put death.

**Avicenna** · 05-01-2007, 14:23

Forcing you to do it by integration is evil.

Easy way out is find the volume of the cone and subtract the cut off top bit.

**naut** · 05-01-2007, 14:42

Originally Posted by The_Mark

I'm just about to graduate from the Finnish equivalent of high school

I hope the you get the results you wanted. I've got half a year left of my schooling.

Originally Posted by The_Mark

The bowl assignment doesn't sound that difficult.

It's just a bit confusing.
V = π∫ a/2 to a (a^2 - y^2) dy
= π [(a)^3/3 - (y)^3/3] a/2 to a
= π/3 {a^3 - (3(a)^3)/8 - a^3 + (8(a)^3)/8}
= π/3 {(5(a)^3)/8}
= (5π(a)^3)/24

Originally Posted by Avicenna

Forcing you to do it by integration is evil.

But strangely satisfying if you get it right.