- #1

Raziel2701

- 128

- 0

## Homework Statement

Given the volume of a 2-sphere in a 3-sphere geometry,

[tex]V=4\pi a^3[\frac{1}{2}\arcsin (r/a) -\frac{r}{2a}[1-(\frac{r}{a})^2]^{(1/2)}][/tex], derive the 1st order correction when r/a<<1

I am also given that this is approximately [tex]V\approx\frac{4\pi r^3}{3}[1+()][/tex]

where inside the blank parenthesis should read "corrections of order (r/a)^2

## The Attempt at a Solution

So since r/a<<1 I figure that the only important term should be the arcsine and that I should expand it, but if I neglect everything but the arcsine I don't get the approximate expression, I just get the 4pir^3 times the first few terms of the arcsine expansion, not to mention that I am not entirely sure what is meant by corrections of order (r/a)^2 since the arcsine expansion has odd powers.