mensuration - 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

Krishna (last edited 2 years ago) (Expert, Educator @Qalaxia)

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