if V(r)=(4/3)(pi)r^3 find

V(2r)
------
V(r)

I'm very confused on how to solve this function. Could someone guide me through this?

Please can some one help

since V is proportional to r^3,

V(2r)/V(r) = 2^3

gather all the constants into a single k, and you have

V(r) = kr^3
V(2r) = k(2r)^3 = k(2^3)(r^3) = 2^3*V(r)

Sure! I can help you with that.

To solve the function, we need to substitute the value of 2r into the original function, V(r), and then divide it by the original function itself, V(r).

Let's start by substituting 2r in place of r in the formula V(r):

V(2r) = (4/3)(pi)(2r)^3

Now, simplify the equation:

V(2r) = (4/3)(pi)(8r^3)
= (32/3)(pi)(r^3)

Next, we need to find V(r) by substituting r in place of r in the original formula:

V(r) = (4/3)(pi)(r^3)

Now, divide V(2r) by V(r):

V(2r) / V(r) = ((32/3)(pi)(r^3)) / ((4/3)(pi)(r^3))

The (pi) and (r^3) terms will cancel out, leaving us with:

V(2r) / V(r) = 32/4

Simplifying further, we get:

V(2r) / V(r) = 8

Therefore, the ratio of V(2r) to V(r) is 8.

I hope this helps! Let me know if you have any more questions.