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

Question

3314 views around the world

You can reuse this answer
Creative Commons License

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, la, ma)#

# = f(l, m)a^3#

#= k a^3#, where #k =f(l,m)#

Example:

Volume of an ellipsoid, #V = (4/3)pi a b c#.

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

#V = (4lm)/3pi a^3#.

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

#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..