Krishna
0

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

h - height

Step 2: Make a note of the given information

Given that,

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