Answer: Option C
Let the radius and height of the cone be 3x and 4x respectively
Then,
$$\eqalign{
& \frac{1}{3} \times \frac{{22}}{7} \times {\left( {3x} \right)^2} \times 4x = \frac{{2112}}{7} \cr
& \Rightarrow \frac{{264}}{7}{x^3} = \frac{{2112}}{7} \cr
& \Rightarrow {x^3} = \frac{{2112}}{{264}} \cr
& \Rightarrow {x^3} = 8 \cr
& \Rightarrow x = 2 \cr} $$
∴ Radius = 6 cm, Height = 8 cm
Slant height :
$$\eqalign{
& = \sqrt {{6^2} + {8^2}} \,cm \cr
& = \sqrt {100} \,cm \cr
& = 10\,cm \cr} $$