Step 1: Recall the formulas of volume of cylinder and cone

                        Volume of cylinder = \pi (r_1)^2 h_1

                        Volume of cone    = \frac{1}{3} \pi (r_2)^2 h_2

                              Where r - radius

                                        h - height

Step 2: Make a note of the given information    

              Given that,

                    Radius of cone = radius of cylinder

                    Height of cone  = Height of cylinder

          We have show that, volume of cylinder : volume of cone = 3 : 1

Step 3: Showing that volumes of cylinder and cone are in the ratio of 3:1  

                   =   \frac{volume\ of\ cylinder}{volume\ of\ cone}

                   =    \frac{\pi r_1^2 h_1}{\frac{1}{3} \pi r_2^2 h_2}

                   =   \frac{\pi h_1}{\frac{1}{3} \pi h_2}                      \because r_1 = r_2

                  =     \frac{\pi }{\frac{1}{3} \pi}                        \because h_1 = h_2

                  =      \frac{3}{1}

                Hence, their volumes are in the ratio 3 : 1