# A Level maths - Fractional indices help

Could anyone help with the following question:

A sphere of radius R cm has area A cm^2 and volume V cm^3. Show that A=kV^(3/2) where k=cuberoot(36pi).

I have got the volume equation in terms of R where R=cuberoot(3V/4pi) and substituted it into the area equation which gives A=pi[cuberoot(3V/4pi)]^2. Not sure what to do next to get it into the correct form.
Original post by xj824
Could anyone help with the following question:

A sphere of radius R cm has area A cm^2 and volume V cm^3. Show that A=kV^(3/2) where k=cuberoot(36pi).

I have got the volume equation in terms of R where R=cuberoot(3V/4pi) and substituted it into the area equation which gives A=pi[cuberoot(3V/4pi)]^2. Not sure what to do next to get it into the correct form.

The surface area of a sphere is 4 pi r^2. Correct that and simplify the expression and it should work. I guess your expression should be A = kV^(2/3)?
(edited 9 months ago)
Original post by xj824
Thanks, is it not possible to solve using only the volume and area equations since those are the ones relating to the variables in the question?

Not sure what youre asking. Youre doing the right thing but correct the area and simplify the expression to get k.
Original post by mqb2766
Not sure what youre asking. Youre doing the right thing but correct the area and simplify the expression to get k.

Could you please explain how to simplify the expression 4pi[cuberoot(3V/4pi)]²? I do not know how to simplify it.
Original post by xj824
Could you please explain how to simplify the expression 4pi[cuberoot(3V/4pi)]²? I do not know how to simplify it.

The answer for k is in terms of the cube root, so you need to take the 4 pi inside the cube root but first apply the square to whats inside. You have roughly
a b^(2/3)
This would become
(a^3b^2)^(1/3)
which should simplify using the usual rules.
(edited 9 months ago)