# How do you write a general formula to describe each variation if V varies directly with x^3; v= 36(pie) when x=3?

Jul 16, 2016

#### Explanation:

If V has three parameters, V = V (a, b, c,). Further, if their

proportions, in a units, are a : b : c = 1 : l : m, then

$V = V \left(a , l a , m a\right)$

$= f \left(l , m\right) {a}^{3}$

$= k {a}^{3}$, where $k = f \left(l , m\right)$

Example:

Volume of an ellipsoid, $V = \left(\frac{4}{3}\right) \pi a b c$.

Here, if b = la and c = m a,

$V = \frac{4 l m}{3} \pi {a}^{3}$.

Given that $V = 36 \pi$, when a =3, m is given by

$36 \pi = 36 l m \pi$. So, lm =1. And the semi axes of the ellipsoid

become a, la and a/l., with l at your choice.

There is scope for giving quite a number examples, like, cube and

tetrahedron..