Which formula you reckon?!

**User Name** · May 24th 2008, 05:06 PM

Hi guys which formula suit this Question?
thanks

**Soroban** · May 24th 2008, 06:26 PM

Hello, User Name!

I'll number the formulas like this: . $\begin{array}{cc} (1) & (2) \\ (3) & (4) \\ (5) \end{array}$

Formula (1): . $V \;=\;\pi\left(\frac{a+b}{2}\right)^2$
. . $\pi r^2$ is the area of the circle. . $\frac{a+b}{2}$ is the average of the two radii.

Therefore, (1) gives the area of the "average circle".
. . I seriously doubt that this happens to be the volume of the doughnut.

Formula (3): . $V \:=\:\frac{\pi}{3}(a^3 + b^3)$
. . $\frac{4}{3}\pi r^3$ is the volume of a sphere.

. . We have: . $\frac{1}{4}\left[\frac{4}{3}\pi a^3 + \frac{4}{3}\pi b^3\right]$

This is the volume of a sphere of radius $a$
. . plus the volume of a sphere of radius $b$
. . divided by 4.

This is too large to be the volume of the doughnut.

Formula (4): . $V \;=\;\pi^3(b^2-a^2)$

We have: . $\pi^2\left(\pi b^2 - \pi a^2\right)$

. . $\pi b^2$ is the area of the outer circle.
. . $\pi a^2$ is the area of the inner circle.
. . $\pi b^2 - \pi a^2$ is the area of the "ring".

I don't think multiplying by $\pi^2$ will give us the volume of the dougnut.

Formula (5): . $V \;=\;\frac{\pi^2}{3}(a + b)^3$
We have: . $\frac{\pi}{4}\left[\frac{4}{3}\pi (a+b)^3\right]$

This the volume of a sphere of radius $a+b$ ... (quite large!)
. . multipled by $\frac{\pi}{4}$

This is far too large to be the volume of the doughtnut.

By elimination, . $(2)\;\;V \:=\:\frac{\pi^2}{4}(a+b)(b-a)^2$ .is the volume of the doughnut.

**User Name** · May 24th 2008, 06:39 PM

Thanks Soroban Once again

I think Your right as usual

Thread: Which formula you reckon?!

LinkBack

Thread Tools

Display

Which formula you reckon?!

Similar Math Help Forum Discussions

how do you prove determinant expand by the Leibniz formula or the Laplace formula ...

Phase calculation formula - can't even use the correct formula properly!!

Finding the formula to an inversely proportional formula?

Complicated Algebra, though I reckon theres a simple answer!

Velocity formula from a position formula

Search Tags