A cylinder and cone have bases of equal radii and are of equal heights. Show that their volumes are in the ratio of 3:1

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