ClassX Video Lessons Youtube Channel Smile and Learn English Circle, Circumference and Number Pi – Compilation Video
Welcome to Smile and Learn! Have you ever noticed how many circles are around you? Think about a Ferris wheel or a bicycle wheel. Today, we’re going to explore two important shapes: the circle and the circumference.
The circumference is a curved line that goes all the way around a circle. Every point on this line is the same distance from the center. Look around you—can you spot any circumferences? How about a ring or a hoop?
The circle is the entire space inside the circumference. So, when you see a coin or a pizza, you’re looking at a circle. The main difference is that the circumference is just the line around the circle, while the circle includes everything inside that line.
Since the circumference is a line, we measure its length in units like inches or miles. On the other hand, the circle is a flat shape, so we measure its area in square units, like square inches or square miles.
Now that you know the parts, let’s talk about a special number called pi.
Pi (π) is a famous number that helps us understand circles. It shows the relationship between the circumference and the diameter of any circle. If you measure how many times the diameter fits around the circumference, you’ll find it’s a little more than three times. That’s why pi is approximately 3.14.
Pi is the same for every circle in the world! You can check this yourself. Measure the circumference and diameter of a round object, like a bike wheel. Divide the circumference by the diameter, and you’ll get about 3.14.
Did you know pi is an infinite number? It starts with 3.14159 and goes on forever! But for everyday use, we just say 3.14.
To find the length of a circumference, you can use pi. Remember, the diameter is twice the radius. The formula to calculate the circumference is:
For example, if a circle has a radius of 2.36 inches, its circumference is about 14.82 inches. If you need to wrap a box with a circular top, and the radius is 4 inches, you’ll need about 25 inches of string.
In another example, if a fountain has a diameter of 29.5 feet, the mayor would need about 92.71 feet of fencing to go around it.
Understanding pi and how to calculate the circumference is important in many fields like construction and engineering. Try measuring some circles around you and see how pi works!
Did you enjoy learning about circles and pi? There are so many more exciting things to discover! Keep exploring and learning!
Look around your home or classroom and find as many circular objects as you can. Measure their diameters and circumferences using a ruler or tape measure. Calculate the ratio of the circumference to the diameter for each object and see how close you get to pi (3.14). Share your findings with the class!
Create a piece of art using circles! Use different sizes of circular objects to trace and cut out circles from colored paper. Arrange them creatively on a poster board. Label the radius, diameter, and circumference of each circle. Display your artwork and explain the parts of a circle to your classmates.
Make a bracelet that represents the digits of pi! Use different colored beads to represent each digit (e.g., red for 1, blue for 2). String the beads in the order of pi (3.14159…) and wear your bracelet as a reminder of this special number. Share the meaning of your bracelet with friends and family.
Participate in a relay race where each team member solves a problem related to circles. Problems can include calculating the circumference, area, or identifying parts of a circle. Work together to complete all the problems as quickly as possible. The first team to finish correctly wins!
Write a short story or poem about pi and its importance in understanding circles. Include characters like a curious mathematician or a magical circle that helps explain the concept of pi. Share your story with the class and discuss how pi is used in real-life situations.
Here’s a sanitized version of the provided YouTube transcript:
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Welcome to Smile and Learn! Can you see that wheel over there? Look at that Ferris wheel! Today, we’re going to tell you about two geometric shapes that you can see everywhere: the circle and the circumference.
The circumference is a curved, closed flat line whose points are the same distance from the center. Look around you. Do you see any circumferences? That’s right, this ring or this hoop!
The circle is a plane figure whose boundaries are a circumference. Look around you again. Do you see any circles? That’s right, this coin or this pizza!
The difference between a circumference and a circle is that the circumference is the line around the circle, while the circle is everything the circumference contains. In other words, the circle is inside the circumference.
As you have been able to see, the circumference is a line, which is why we measure its length in yards, inches, or miles. However, the circle is a plane figure, which is why we measure its surface in square yards, square inches, or square miles.
We can distinguish the following elements in a circumference and a circle:
– The center is the point from which all the points of the circumference are the same distance.
– The radius is a segment that connects the center with any point of the circumference.
– The diameter is a segment that connects two points of the circumference, passing through the center. It divides the circle into two parts. As you can see, the diameter is twice the radius.
– The chord is the segment that connects any two points of the circumference.
– The arc is the part of the circumference that lies between two points.
– The sector is the region between two radii and their arc.
Let’s recap the parts of the circle and the circumference: the center, the radius, the diameter, the chord, the arc, and the sector. Well done!
Now, let’s introduce a very famous number found in all circumferences and circles: pi. Pi is a mathematical constant that indicates the relation between the perimeter and the diameter of a circumference.
But how can we describe this relation? It’s about fitting the diameter as many times as possible into the perimeter of the circumference. Let’s look here: one, two, three, and a little bit more. That’s it! We can fit three diameters into the circumference in a small part, plus a little extra. That’s why we know that pi equals approximately 3.14.
We say that it’s a constant because the number pi is the same for every circumference in the world. In other words, this number is always equal to 3.14. Would you like to check? It’s very simple! Look for a measuring tape and measure the perimeter of a round object you have at home, for example, the wheel of this bike.
If the perimeter of this wheel is 98.8 inches and its diameter is 31.4 inches, if we divide 98.8 by 31.4, we’ll get 3.14.
Now measure the perimeter of this swimming pool. If the perimeter of this circular swimming pool is 51.5 feet and its diameter is 16.4 feet, if we divide 51.5 by 16.4, we’ll also get 3.14.
It’s like magic! The result we get every time we divide the perimeter by the diameter of any circle in the world will always be 3.14. This happens because pi is a mathematical constant.
There’s a very interesting fact we haven’t told you about yet: pi is represented by this Greek letter and is an infinite number: 3.1415926535897932384, and the digits go on forever. In everyday life, this number is shortened to 3.14 to make calculations easier.
Today, we learned that number pi is one of the most important mathematical constants. Many architecture, mechanics, or engineering projects wouldn’t be possible without the number pi.
Now, let’s talk about how to calculate the length of the circumference. The length of a circumference can also be referred to as the perimeter of a circle.
To start with, let’s recap some elements of the circumference: the center, the radius, and the diameter. Remember that the diameter is twice the radius, or in other words, the radius is half the diameter.
The length of the circumference equals twice the radius multiplied by pi, or the diameter of the circumference multiplied by pi. Remember that pi is approximately 3.14.
Let’s look at some examples. If this circumference has a radius of 2.36 inches, to calculate its length, we should multiply the radius by 2 and then by pi. The length of this circumference equals approximately 14.82 inches.
In a real-life situation, if Mark wants to decorate a box of chocolates using some wrapping string and the radius of the circumference of the box measures 4 inches, he needs to calculate the length of this circumference. He would multiply the radius by 2 and by pi. Mark needs to buy approximately 25 inches of wrapping string to decorate the box of chocolates.
Let’s look at another example. If the mayor wants to put a fence around the fountain of the village, and the fountain has a circular shape with a diameter of 29.5 feet, he needs to calculate the length of this circumference. He would multiply the diameter by pi. The mayor needs to buy approximately 92.71 feet of fencing material to surround the fountain.
For every circumference in the world, pi is always the same number, which is approximately 3.14. If you want to learn more about it, watch our video about the number pi.
Knowing how to calculate the length of a circumference is very important in construction, mechanics, or engineering. How would you like to try with another example?
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This version removes any informal language, repetitive phrases, and maintains a clear and educational tone.
Circle – A round shape where all points are the same distance from the center. – The teacher drew a circle on the board and asked us to find its radius.
Circumference – The distance around the edge of a circle. – We used a string to measure the circumference of the bicycle wheel.
Pi – A special number approximately equal to 3.14, used to calculate the circumference and area of circles. – To find the circumference of the circle, we multiplied the diameter by pi.
Radius – The distance from the center of a circle to any point on its edge. – The radius of the circle is half of its diameter.
Diameter – The distance across a circle through its center, twice the radius. – We measured the diameter of the pizza to see if it would fit on the plate.
Chord – A straight line connecting two points on a circle. – The teacher asked us to draw a chord inside the circle on our worksheet.
Arc – A part of the circumference of a circle. – We learned how to measure the length of an arc using a protractor.
Sector – A part of a circle enclosed by two radii and an arc. – The slice of pie looked like a sector of a circle.
Measure – To find the size, length, or amount of something using standard units. – We used a ruler to measure the length of the rectangle.
Area – The amount of space inside a shape, measured in square units. – We calculated the area of the rectangle by multiplying its length by its width.
