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Why tree trunks are cylindrical shapes? | English
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Have you ever wondered why the tree trunks are shaped like a perfect cylinder. Or why the kitchen containers with greatest volumes have round shape? Today we will learn about this with the help of an interesting math’s activity using three post cards.
If you don’t have postcards, you can use three cut-outs having same dimensions from a card sheet.
The shape of these post cards is a perfect rectangle. Now let’s look at the dimensions of the post card. Length of this postcard is L= 14.5 cm and Breadth B = 9.5 cm. The Area of the rectangle is length x breadth so the area of this card is 14.5 x 9.5 = 137.75 cm 2 . All three postcards are identical and thus have the same length, breadth and surface area. Now fold three postcards along the width to make three shapes.
1. A Regular cylinder (with circular base)
2. A Square base cylinder (a cuboid)
3. A Triangle base cylinder (a prism)
Mark A on the circular base cylinder, Mark B on Square base cylinder and Mark C on triangular base
Cylinder you have made three cylinders using similar postcards with different shape for the base. Even though Shapes are different but the height for all three cylinders is same. Suppose I want to calculate which cylinder has greatest volume? How can I do that without actually calculating the volume? Let’s fill something in all three cylinders to find out. We have different pulses. Make each cylinder stand vertically in a plate and fill all three cylinder completely with pulses. Remove the cylinder slowly to form a small pile of pulses. The circular cylinder could fit most amount followed by the square cylinder and the triangle base cylinder had the least amount. Let’s calculate actual volume of all three shapes. The volume will be calculated using the formula area of the base x height.
Volume of 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 Volume of Cylinder B = side 2 x h (side of square is 3.62 cm, h = 9.5 cm)
= 3.62 cm x 3.62 cm x 9.5cm
=124.49 cm3
Volume of Volume of Cylinder C = 1/2 x base x height x h (side of square is 3.62 cm, h = 9.5 cm)
= ½ x 4.8 cm x 4.2 cm x 9.5cm
=95.76 cm3
As seen by the calculations, circular base cylinder has the highest volume. As the height of all cylinders is same, this also means that for same length (14.5cm) as perimeter or circumference, a circle has maximum area. As the circular cylinder has maximum volume as compared to other shapes, tree trunks tend to grow into a cylindrical shape so that they can fit most material with least surface area. Same is the logic for circular kitchen containers. This idea also holds true for other objects such as planets or stars which will be discussed in another video.
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, Abha Mahajan, Sayali Deshpande, Neha Apte
If you don’t have postcards, you can use three cut-outs having same dimensions from a card sheet.
The shape of these post cards is a perfect rectangle. Now let’s look at the dimensions of the post card. Length of this postcard is L= 14.5 cm and Breadth B = 9.5 cm. The Area of the rectangle is length x breadth so the area of this card is 14.5 x 9.5 = 137.75 cm 2 . All three postcards are identical and thus have the same length, breadth and surface area. Now fold three postcards along the width to make three shapes.
1. A Regular cylinder (with circular base)
2. A Square base cylinder (a cuboid)
3. A Triangle base cylinder (a prism)
Mark A on the circular base cylinder, Mark B on Square base cylinder and Mark C on triangular base
Cylinder you have made three cylinders using similar postcards with different shape for the base. Even though Shapes are different but the height for all three cylinders is same. Suppose I want to calculate which cylinder has greatest volume? How can I do that without actually calculating the volume? Let’s fill something in all three cylinders to find out. We have different pulses. Make each cylinder stand vertically in a plate and fill all three cylinder completely with pulses. Remove the cylinder slowly to form a small pile of pulses. The circular cylinder could fit most amount followed by the square cylinder and the triangle base cylinder had the least amount. Let’s calculate actual volume of all three shapes. The volume will be calculated using the formula area of the base x height.
Volume of 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 Volume of Cylinder B = side 2 x h (side of square is 3.62 cm, h = 9.5 cm)
= 3.62 cm x 3.62 cm x 9.5cm
=124.49 cm3
Volume of Volume of Cylinder C = 1/2 x base x height x h (side of square is 3.62 cm, h = 9.5 cm)
= ½ x 4.8 cm x 4.2 cm x 9.5cm
=95.76 cm3
As seen by the calculations, circular base cylinder has the highest volume. As the height of all cylinders is same, this also means that for same length (14.5cm) as perimeter or circumference, a circle has maximum area. As the circular cylinder has maximum volume as compared to other shapes, tree trunks tend to grow into a cylindrical shape so that they can fit most material with least surface area. Same is the logic for circular kitchen containers. This idea also holds true for other objects such as planets or stars which will be discussed in another video.
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, Abha Mahajan, Sayali Deshpande, Neha Apte
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