Understand Circles with Carts and Wheel Revision Notes and Worksheets
Circles
A circle is a collection of points which are at an equal distance from a certain point in a plane.
A circle is a round shape figure in a plane.
Examples - Wheels of a cart, watch, coin, disk, dishes, rings, bracelets, earrings, bangles, buttons etc.
Image: Circle
Parts of a Circle
Centre
A fixed point at an equal distance from every point on the circumference of the circle is known as the centre.
Image: Circle with center O
Radius
The line joining the centre and any point on the circumference of the circle is called the radius of the circle.
The radius is half of the diameter of a circle.
Radius of the circle =$\frac{\text{diameter of the circle}}{2}$
Image: Circle with radius OA
Solved Example
1: Find the radius of a circle if the diameter of the circle is 10cm.
Ans: The radius of a circle is half of the diameter of the circle.
Radius of the circle = $\frac{\text{diameter of the circle}}{2}$
Diameter of the circle = 10 cm
Image: Circle with a diameter of 10cm
The radius of a circle = $\frac{\text{10}}{2}$
The radius of a circle = 5 cm
Therefore, the radius of the circle is 5 cm.
2: If the diameter of the circle is 12 cm then find the radius of the circle.
Ans: The radius of a circle is half of the diameter of the circle.
Radius of the circle = $\frac{\text{diameter of the circle}}{2}$
Diameter of the circle = 12 cm
Image: Circle with diameter AB = 12cm
The radius of a circle = $\frac{\text{12}}{2}$
The radius of a circle = 6 cm
Therefore, the radius of the circle is 6 cm.
3. Diameter
The line that joins the two boundary points of a circle and passes through the centre is known as the diameter.
The diameter is twice the radius of a circle.
Diameter = 2 x Radius of a circle
Image: Circle with diameter AB
Solved Example
1: Find the diameter of a circle if the radius of the circle is 10cm?
Ans: The diameter of a circle is twice the radius of a circle.
Diameter =2 x Radius of a circle
Image: Circle with radius OA = 10 cm
Diameter = 2 x 10 cm
Diameter = 20 cm
Therefore, the diameter of a circle is 20 cm.
2: If the radius of a circle is 7 cm then find the diameter of the circle.
Ans: The diameter of a circle is twice the radius of a circle.
Image: Circle with radius OA = 7 cm
Diameter = 2 x Radius of a circle
The diameter of a circle = 2 x7 cm
The diameter of a circle = 14 cm
Therefore, the diameter of a circle is 14 cm.
Semicircle
The diameter of a circle divides the circle into two equal halves and each half is known as a semicircle.
If two semicircles are combined together then it will be equivalent to a complete circle.
Image: Semi circle
Circumference
The circumference is the complete distance of a single round around the circle.
The circumference is the length of the boundary of a circle.
Circumference of the circle= 2 x π x Radius of the circle
Circumference of the circle = π x Diameter of the circle
Image: Circle with radius OA and diameter AB
Solved Example
1: If the radius of a circle is 7 cm then find the circumference of the circle.
Ans: The circumference is the length of the boundary of a circle.
Image: Circle with radius OA = 7 cm
The circumference of the circle = 2 x π x 7 cm
The circumference of the circle $-2\times \;{\frac{\text{22}}{7}}\;\times 7$ cm
The circumference of the circle= -2 x 22cm
The circumference of the circle = 44 cm
2: Find the circumference of a circle if the diameter of the circle is 10cm?
Image: Circle with a diameter of 10cm
Ans: The circumference is the length of the boundary of a circle.
Circumference of a circle =π x Diameter of a circle
Circumference of a circle= ${\frac{\text{22}}{7}}\;\times 10$cm
Circumference of a circle= ${\frac{\text{220}}{7}}$cm
Circumference of a circle = 31.43 cm
Drawing Circles
To draw a circle of a certain radius we need a compass, a pencil and a scale.
Step 1: Set the compass needle at 0 on the scale and open the compass equal to the required radius.
Image: Measurement of the radius
Step 2: Set the compass needle in the centre of a paper sheet.
Image: Setting the compass needle
Step 3: Move the pencil around the fixed needle to draw a circle.
Image: Drawing Circle
Example 1: Draw a circle of 6 cm using a compass and pencil.
Ans: Step 1: Set the compass needle at 0 on the scale and open the compass equal to 6 cm.
Image: Measurement of the radius = 6cm
Step 2: Set the compass needle in the centre of a paper sheet.
Image: Setting the compass needle
Step 3: Move the pencil around the fixed needle to draw the required circle.
Image: Drawing Circle
Practice Questions
1. If three friends have different ropes of different lengths. They have made different circles using the ropes which are given below.
Image: Circles with different radius
(i) which is the smallest circle?
(ii) Which is the largest circle?
Ans:
(i) Nitin’s Circle
(ii) Arun’s Circle
2. If the diameter of a circle is 20 cm then find the radius and circumference of the circle.
Ans: Radius of the circle = 10 cm, Circumference of the circle = 62.86 cm
3. Name the following in the given circle.
(i) Centre
(ii) Radius
(iii) Diameter
Image: Circle with radius OB and diameter AC
Ans :
(i) O
(ii) AO or OB or OC
(iii) AC
Importance of CBSE Class 4 Maths Chapter 8 Carts and Wheels
The chapter on Carts and Wheels is a unique one in the Class 4 Maths syllabus. This chapter introduces a shape that does not have any straight lines. Previously, students have studied shapes that had sides. Now they will learn what a circle is. Here is why this chapter is very important for children.
The introduction of curved shapes in this chapter will give new ideas to the students. They will prepare a conceptual base related to circles using daily objects and will become confident to learn advanced geometrical concepts in the future years.
This chapter explains how a circle can be drawn using just a rope and fixing it on a particular point. It offers a medium of experiential learning for the Class 4 students.
The Carts and Wheels summary suggests that this chapter teaches how curves can make a symmetrical shape.
Students will also learn how to draw smaller and bigger circles by simply reducing and increasing a radius.
Benefits of Vedantu’s Carts and Wheels Class 4 Worksheets and Revision Notes
Proper explanation of the concepts in simpler language to help you understand faster
Execution of the exercise problems in a simpler way
Referring to Carts and Wheels Class 4 worksheets answers will help determine the right ways to solve problems
Easy and quick preparation before an exam
Accurate information as per the CBSE Class 4 standards
Explaining how to make designs with circles using geometric tools
Learning from the round things around you made easier and more interesting
Understanding the different parts and features of a circle
Smooth Studying with Class 4 Maths Chapter 8 Carts and Wheels PDF
In wrapping up the Class 4 CBSE Maths Chapter 8 on 'Carts and Wheels,' these notes provide a foundational understanding of concepts related to measurements, distances, and their application in real-life scenarios. Exploring these notes equips students with essential mathematical skills, fostering a practical understanding of measurements and their relevance in our daily lives. Mastering these concepts lays a strong foundation for further mathematical exploration and problem-solving.
FAQs on Carts and Wheels Class 4 Notes CBSE Maths Chapter 8 (Free PDF Download)
1. What is a diameter?
The diameter is the longest chord that fits inside a circle. As per the definition of radius in Class 4th Maths Chapter 8, diameter is equal to two times the radius of a circle.
2. What is the circumference of a circle?
When you perform the activity of making a circle with a rope, you will draw a line on the ground with a stick. The line you draw is the circumference of the circle. It gives the round shape to a circle.
3. Is the ball a circle?
A ball is an object that looks like a circle when you draw it on paper. A circle is a shape. Hence, a ball is called a sphere, a regular round object.