Which cylinder holds more? | English

Friends today we will learn interesting activity about math’s using two post cards. If you don’t have the postcards then you can use two similar cut-outs from a card sheet.


Here I have two Postcards. Back in the day, people used to send messages to their friends and relatives using Postcards and today we will learn an interesting mathematical activity using them. If I ask you, what is the shape of this postcard? You may say it’s a rectangular shape which is Correct as this is a perfect rectangle. Now what is the Area of this rectangle? Area of the rectangle is calculated by the formula length x breadth. To get the area of this postcard we need to measure length and breadth. Length of this postcard is L= 14.5 cm and Breadth B = 9.5 cm so the area of this card is 14.5 x 9.5 = 137.75 cm 2 . Here I have two identical postcards so the area of both postcards will be same. Now I am folding one postcard along the width and another and another one along the length and make two cylinders. We will use a tape to join two edges. This will make two cylinders one fat and short and another tall and thin cylinder. As you know both the cylinders have made from the same post cards so they must have the same surface Area. Mark A on the fat cylinder and B on thin cylinder. Suppose I wants to fill some material in both cylinders, what you think, which cylinder will hold more of the material? In other words, which cylinder has greater volume? You have three options
1. Cylinder A
2. Cylinder B
3. Cylinder A and B both have same volume.
Most people says both have same volume and will hold the same amount of material as they are the same surface area. Now let’s test this with some pulses. Take two plates and make both cylinder stand vertically in each of them. Fill both the cylinders completely with pulses and then remove the cylinders slowly. There will be a pile of pulses in both plates. Surprisingly the fat cylinder seems to contain more amount of the pulses than the thin cylinder despite the same surface area. Let’s confirm if this is indeed the case.
Keep the fat cylinder in a plate and place the thin cylinder inside the fat one. Fill the thin cylinder with pulses up to the brim. Now gently remove the thin cylinder so that the pulses occupy the volume in the outer one. What do we see? The fat cylinder is only about 2/3 rd filled with the pulses. This confirms that volume of fat cylinder is higher. Let’s measure the volume of both the cylinders
Volume of the cylinder is given by the formula πr 2 h
Hence, Volume of Cylinder A = πr 2 h (π – 3.14, r – 2.30, h – 9.5 cm)
= 3.142 x 2.3 cm x 2.3cm x 9.5cm
=157.90 cm3
Volume of Cylinder B= πr 2 h (π – 3.14, r – 1.5, h – 14.5 cm)
= 3.142 x 1.5 cm x 1.5cm x 14.5cm
=102.50 cm3
Thus on calculating the actual volumes, we see the volume of the fat cylinder is greater than the tall cylinder by about 1.5 times. This is because volume of cylinder increases proportional to the square of the radius of the cylinder.
If you see the cylindrical containers in the kitchen, they designed in such a way that the volume is maximum for the given surface area that is, the amount of raw material required. Thus they usually increase the area of circle and not the height of the container. I hope you enjoyed this activity and learnt something new. For more such fun with hands-on science and math’s activities please visit our YouTube channel IISER Pune science activity centre. Have fun!

Team: Ashok Rupner, Chaitanya Mungi, Shanti Pise, Neha Apte , Sayali Deshpande