Calculating the Volume of a function on the sphere

Question

As part of a question in calculus homework, I have to calculate:

$Vol_n(M_C(f))$, when

1. $f:S^{n-1}_+\rightarrow \mathbb{R}$ (when $S^{n-1}_+=\left\{x\in S^n: \forall i\in [1,n], <x,e_i>\geq 0\right\}$) is defined by $f(y)=\frac{1}{<a,y>^n}$, for a constant vector $a\in \mathbb{R}^n$

2. $M_C(f)=\left\{x\in S^{n-1}_+: f(x)=C\right\}$

and I currently have no idea how to calculate this from $Vol_n(M_C(f))=\int_{M_C(f)}1dx$.

Thanks for the help!