Answer: Option C
Let the radius of the cone be R cm
Then,
$$\eqalign{
& \frac{1}{3}\pi \times {R^2} \times 75 = \frac{2}{3}\pi \times 6 \times 6 \times 6 \cr
& \Rightarrow {R^2} = \left( {\frac{{2 \times 6 \times 6 \times 6}}{{75}}} \right) \cr
& \Rightarrow {R^2} = \frac{{144}}{{25}} \cr
& \Rightarrow {R^2} = \frac{{{{\left( {12} \right)}^2}}}{{{{\left( 5 \right)}^2}}} \cr
& \Rightarrow R = \frac{{12}}{5} \cr
& \Rightarrow R = 2.4\,cm \cr} $$