The volume of a hemisphere is given by
$$volume=\frac{2}{3}\pi r^3$$
where r is the radius.
The desired volume of clay will be the difference between the outer and inner hemispherical volumes, so:
$$k\pi^3=\frac{2}{3}\pi8.2^3-\frac{2}{3}\pi7.7^3 = \frac{2}{3}\pi(8.2^3-7.7^3)$$
The exact value of k is therefore
$$k=\frac{2}{3}\frac{(8.2^3-7.7^3)}{\pi^2}$$
Numerically, the approximate value is:
$${\mathtt{k}} = {\frac{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right){\mathtt{\,\times\,}}\left({{\mathtt{8.2}}}^{{\mathtt{3}}}{\mathtt{\,-\,}}{{\mathtt{7.7}}}^{{\mathtt{3}}}\right)}{{{\mathtt{\pi}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{k}} = {\mathtt{6.405\: \!862\: \!967\: \!147\: \!401\: \!7}}$$
or k ≈ 6.41 (it will have units of cm3)
I would say this topic is Geometry.