The radii of the bases of two cylinders are in the ratio 3 : 4 and their height are in the ratio 4 : 3. The ratio of their volume is :

Answer: Option C

Let their radii be 3x, 4x and heights be 4y, 3y
Ratio of their volumes :
$$\begin{array}{rl}& =\frac{\pi \times {\left(3x\right)}^2\times 4y}{\pi \times {\left(4x\right)}^2\times 3y}\\ & =\frac{36}{48}\\ & =\frac{3}{4}Or3:4\end{array}$$