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

Kennedy Adams · Accepted Answer

undefined The general formula to describe the variation is V = kx^3, where k is the constant of variation. To find the value of k, we can substitute the given values into the equation. When x = 3 and V = 36π, we have 36π = k(3^3). Simplifying, we get k = 4π. Therefore, the specific formula for this variation is V = 4πx^3.

Avery Alexander · Answer

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..