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

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Answer 1 · 2016-07-16T16:45:07

I have used a instead of x. Please read the 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

$V = V (a, l a, m a)$ $V = V( a, la, ma)$

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

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

Example:

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

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

$V = \frac{4 l m}{3} π a^{3}$ $V = (4lm)/3pi a^3$ .

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

$36 π = 36 l m π$ $36pi = 36 l m pi$ . 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..