1. Circles and circumference (compass)
Good Afternoon!
Today we will be learning about
Circles and circumference (compass)
Let’s warm up :
The radii of circles are given. Find is the circumference?
1) 4.8 cm
2) 16 ft
1) cm
2) ft
The diameter of circle are given. Find is the circumference?
3) 31 cm
4) ft
3) 97.34cm
4) 49.5 ft
CONFIDENTIAL

2. Circles and circumference (compass) .
Let’s review what we did in the last session
We learnt about
Circles and circumference (compass) .
Circle: A circle is a shape with all points that are same distance from the center. O
Radius
The circle is named circle O since the center is at point O.
Radius: The radius is a line segment that begins from the centre and touches any point on the circle.
CONFIDENTIAL

3. The Diameter is equal to twice the radius.
Review
Diameter: The distance across a circle through the center is called the diameter.
The Diameter is equal to twice the radius.
Diameter = 2 × Radius O
Diameter
Circumference: The distance around a circle is called the circumference.
The circumference of a circle is also called the perimeter of the circle.
CONFIDENTIAL

4. Review
Lines in a Circle
The name of a line in a circle depends on its position in the circle.
secant
chord
tangent
A secant is a line that passes through any two points on a circle.
A chord is a line that joins two points on the circumference of a circle.
A tangent is a line that touches the circle at only one point.
CONFIDENTIAL

5. Parts of a Circle An arc is a part of the circumference.
Review
Parts of a Circle
An arc is a part of the circumference.
Here, AB is the arc. A B
arc AB O
sector AOB
A sector is the part of a circle between two radii.
Here, AOB is the sector .
CONFIDENTIAL

6. Review
Parts of a Circle
A segment is the part of a circle that is between a chord and the circumference.
segment
semicircle
A semicircle is a half of a circle.
CONFIDENTIAL

7. Review
Circumference
The Circumference is the distance around the edge of the circle.
It is exactly Pi (the symbol is π) times the Diameter, so:
Circumference = π × Diameter
Since the Diameter is equal to twice the radius.
So this is also true:
Circumference = 2 × π × Radius
CONFIDENTIAL

8. The radius of a circle is 2 inches. What is the diameter?
Review
The radius of a circle is 2 inches. What is the diameter?
The radius of a circle = 2 inches
Since the Diameter is equal to twice the radius.
i.e. Diameter = 2 × Radius
Diameter = 2 × Radius
= 2 x 2 inches
= 4 inches
Replace radius with 2.
The diameter of a circle = 4 inches
CONFIDENTIAL

9. The radius of a circle is 2 inches. What is the circumference?
Review
The radius of a circle is 2 inches. What is the circumference?
The radius of a circle = 2 inches
We know that,
Circumference = 2 × π × Radius
Circumference = 2 x π x 2
= 2 x 3.14 x 2
= 12.56
Replace radius with 2.
Replace π with 3.14.
The circumference of a circle = inches
CONFIDENTIAL

10. The diameter of a circle is 5 meters. What is the circumference?
Review
The diameter of a circle is 5 meters. What is the circumference?
The diameter of a circle = 5 meters
We know that,
Circumference = π × Diameter
Circumference = π x 5
= 3.14 x 5
= 15.7
Replace diameter with 5.
Replace π with 3.14.
The circumference of a circle = 15.7 meters
CONFIDENTIAL

11. 2D vs. 3D (Solid Figures) & volume
Let’s start with
2D vs. 3D (Solid Figures) & volume
A 2-dimentional figure is a shape with length and width.
It can be open or closed.
Closed figures: These are those figures that start and end at the same point.
The figures shown above are closed figures.
CONFIDENTIAL

12. The figures shown above are Open figures.
Open figures: These are those figures that do not start and end at the same point.
The figures shown above are Open figures.
CONFIDENTIAL

13. A circle is a closed figure, but it does not have straight sides.
A polygon is a closed 2-dimentional figures with straight sides. They are made of straight lines, and the shape is "closed“.
Polygon (straight sides)
Not a Polygon (has a curve)
Not a Polygon (open, not closed)
A circle is a closed figure, but it does not have straight sides.
A circle is not a polygon.
A polygon can be grouped by the number of sides they have.
CONFIDENTIAL

14. Names of Polygons Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
CONFIDENTIAL

15. A 3-dimentional figure: is a figure with length, width and height.
3-dimensional figure
A 3-dimentional figure: is a figure with length, width and height.
You can describe a 3- dimensional figure by its parts.
vertex
A face is a flat side.
A base is a face on which the figure sits.
An edge is where two faces meet.
A vertex is where 3 or more faces meet.
edge
face
base
CONFIDENTIAL

16. Examples of 3-dimensional figure.
Cube
Cylinder
A cube has 6 faces, 12 edges, 8 vertices
2 circular bases
CONFIDENTIAL

17. Rectangular prism Triangular pyramid Rectangular prism
Triangular pyramid has 4 faces, 6 edges, 4 vertices
Rectangular prism
has 4 faces, 12 edges, 8 vertices
CONFIDENTIAL

18. Net for a square pyramid.
Make a Net
You can make a net for any solid figure.
Net for a square pyramid.
Cube
Triangular Prism
CONFIDENTIAL

19. Volume of a Cuboids Cuboids are a 3-dimensional shape.
It has 3 different measurements.
Height
Width
Depth
The volume of he cube is found using the formula
Volume = Height × Width × Depth
CONFIDENTIAL

20. The dimensions of a Rectangular prism is given. Find its volume.
Height = 6 cm
Width = 4 cm
Depth = 7 cm
We know that the volume of he cube is found using the formula
Volume = Height × Width × Depth
= 6 × 4 × 7
= 168
The volume of a Rectangular prism
= 168 cubic centimeter or cm3.
CONFIDENTIAL

21. BREAK
CONFIDENTIAL

22. Click on the link below for some exciting puzzle
GAME
Click on the link below for some exciting puzzle
CONFIDENTIAL

23. Assignments Identify 3-dimentional figure.
Tell how many faces, edges and vertices it has 1) 2)
1) 4 faces, 6 edges, 4 vertices
2) 6 faces, 12 edges, 8 vertices 3) 4)
3) 1 circular base
4) no face, edge or vertices
CONFIDENTIAL

24. The dimensions of Rectangular prisms are given.
Find their volume.
5) Height = 5 cm
Width = 4 cm
Depth = 6 cm
6) Height = 6 cm
Width = 8 cm
Depth = 11 cm
5) 120 cm3.
6) 528 cm3.
7) Height = 12 cm
Width = 14 cm
Depth = 7 cm
8) Height = 9 cm
Width = 5 cm
Depth = 8 cm
7) 1176 cm3.
8) 360 cm3.
CONFIDENTIAL

25. A 2-dimentional figure is a shape with length and width.
Very Good!
Let's Review
A 2-dimentional figure is a shape with length and width.
It can be open or closed.
Closed figures: These are those figures that start and end at the same point.
The figures shown above are closed figures.
CONFIDENTIAL

26. The figures shown above are Open figures.
Review
Open figures: These are those figures that do not start and end at the same point.
The figures shown above are Open figures.
A polygon is a closed 2-dimentional figures with straight sides. They are made of straight lines, and the shape is "closed“.
A circle is a closed figure, but it does not have straight sides.
A circle is not a polygon.
CONFIDENTIAL

27. A polygon can be grouped by the number of sides they have.
Review
A polygon can be grouped by the number of sides they have.
Name
Sides
Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
CONFIDENTIAL

28. A 3-dimentional figure: is a figure with length, width and height.
Review
3-dimensional figure
A 3-dimentional figure: is a figure with length, width and height.
You can describe a 3- dimensional figure by its parts.
vertex
A face is a flat side.
A base is a face on which the figure sits.
An edge is where two faces meet.
A vertex is where 3 or more faces meet.
edge
face
base
CONFIDENTIAL

29. Examples of 3-dimensional figure.
Review
Examples of 3-dimensional figure.
Cube
Cylinder
A cube has 6 faces, 12 edges, 8 vertices
2 circular bases
Rectangular pyramid
Triangular pyramid
Triangular pyramid has 4 faces, 6 edges, 4 vertices
Triangular pyramid has 4 faces, 12 edges, 8 vertices
CONFIDENTIAL

30. Net for a square pyramid.
Review
Make a Net
You can make a net for any solid figure.
Net for a square pyramid.
Cube
Triangular Prism
CONFIDENTIAL

31. Volume of a Cuboids Cuboids are a 3-dimensional shape.
Review
Volume of a Cuboids
Cuboids are a 3-dimensional shape.
It has 3 different measurements.
Height
Width
Depth
The volume of he cube is found using the formula
Volume = Height × Width × Depth
CONFIDENTIAL

32. The dimensions of a Rectangular prism is given. Find its volume.
Review
The dimensions of a Rectangular prism is given.
Find its volume.
Height = 6 cm
Width = 4 cm
Depth = 7 cm
We know that the volume of he cube is found using the formula
Volume = Height × Width × Depth
= 6 × 4 × 7
= 168
The volume of a Rectangular prism = 168 cm2.
CONFIDENTIAL

33. See you in the next session.
You have done a nice job.
See you in the next session.
CONFIDENTIAL