confidential1 2d vs. 3d (solid figures) and volume grade 4
TRANSCRIPT
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CONFIDENTIAL 1
2D vs. 3D (solid figures) and Volume
Grade 4
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CONFIDENTIAL 2
Let’s warm up :
The radii of circles are given. Find is the circumference?
1) 4.8 cm 2) 16 ft
The diameter of circle are given. Find is the circumference?
3) 31 cm 4) 15.75 ft
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CONFIDENTIAL 3
Circle: A circle is a shape with all points that are same distance from the center.
O
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.
Radius
Let’s review what we did in the last session
We learnt about Circles and circumference (compass) .
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CONFIDENTIAL 4
Diameter: The distance across a circle through the center is called the diameter.
The Diameter is equal to twice the 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.
Diameter = 2 × Radius
Review
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CONFIDENTIAL 5
Lines in a Circle
The name of a line in a circle depends on its position in the circle.
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.
secant
chord
tangent
Review
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CONFIDENTIAL 6
Parts of a Circle
An arc is a part of the circumference.Here, AB is the arc.
A sector is the part of a circle between two radii.Here, AOB is the sector .
AB
arc AB
O
sector AOB
Review
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CONFIDENTIAL 7
Parts of a Circle
A segment is the part of a circle that is between a chord and the circumference.
segment
A semicircle is a half of a circle.
semicircle
Review
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CONFIDENTIAL 8
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
Review
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CONFIDENTIAL 9
The radius of a circle is 2 inches. What is the diameter?
Since the Diameter is equal to twice the radius.
The radius of a circle = 2 inches
i.e. Diameter = 2 × Radius
Diameter = 2 × Radius = 2 x 2 inches
= 4 inches
The diameter of a circle = 4 inches
Replace radius with 2.
Review
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CONFIDENTIAL 10
The radius of a circle is 2 inches. What is the circumference?
We know that,
The radius of a circle = 2 inches
Circumference = 2 × π × Radius
Circumference = 2 x π x 2 = 2 x 3.14 x 2 = 12.56
The circumference of a circle = 12.56 inches
Replace radius with 2.
Replace π with 3.14.
Review
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CONFIDENTIAL 11
The diameter of a circle is 5 meters. What is the
circumference?
We know that,
The diameter of a circle = 5 meters
Circumference = π × Diameter
The circumference of a circle = 15.7 meters
Circumference = π x 5 = 3.14 x 5 = 15.7
Replace diameter with 5.
Replace π with 3.14.
Review
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CONFIDENTIAL 12
Let’s start with2D vs. 3D (Solid Figures) &
volume
A 2-dimensional 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.
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CONFIDENTIAL 13
Open figures: These are those figures that do not start and end at the same point.
The figures shown above are Open figures.
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CONFIDENTIAL 14
A polygon is a closed 2-dimensional 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.
A polygon can be grouped by the number of sides they have.
Polygon (straight sides)
Not a Polygon (has a curve)
Not a Polygon (open, not closed)
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CONFIDENTIAL 15
Name Sides Shape
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Names of Polygons
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CONFIDENTIAL 16
3-dimensional figure
A 3-dimensional figure: is a figure with length, width and height.
You can describe a 3- dimensional figure by its parts.
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.
vertex
face
base
edge
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CONFIDENTIAL 17
Examples of 3-dimensional figure.
Cube
A cube has 6 faces, 12 edges, 8 vertices
Cylinder
2 circular bases
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CONFIDENTIAL 18
Triangular pyramid
Triangular pyramid has 4 faces, 6 edges, 4 vertices
Rectangular prism
Rectangular prism has 4 faces, 12 edges, 8
vertices
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CONFIDENTIAL 19
Make a NetYou can make a net for any solid figure.
Net for a square pyramid.
CubeTriangular Prism
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CONFIDENTIAL 20
Volume of a Cuboids
Cuboids are a 3-dimensional shape.
It has 3 different measurements.
Height
WidthDep
th
The volume of he cube is found using the formula
Volume = Height × Width × Depth
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CONFIDENTIAL 21
The dimensions of a Rectangular prism is given.Find its volume.
Height = 6 cmWidth = 4 cmDepth = 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 cm3.
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CONFIDENTIAL 22
BREAK
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CONFIDENTIAL 23
Title: Format: WebEx Web BrowserDouble-click to edit
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CONFIDENTIAL 24
Assignments
Identify 3-dimensional figure.Tell how many faces, edges and vertices it has
1) 2)
3) 4)
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CONFIDENTIAL 25
The dimensions of Rectangular prisms are given.Find their volume.
5) Height = 5 cmWidth = 4 cmDepth = 6 cm
7) Height = 12 cm
Width = 14 cm
Depth = 7 cm
6) Height = 6 cmWidth = 8 cmDepth = 11
cm
8) Height = 9 cmWidth = 5 cmDepth = 8 cm
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CONFIDENTIAL 26
Very Good!Let's Review
A 2-dimensional 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.
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CONFIDENTIAL 27
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-dimensional 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.
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CONFIDENTIAL 28
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
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CONFIDENTIAL 29
Review
3-dimensional figure
A 3-dimensional figure: is a figure with length, width and height.
You can describe a 3- dimensional figure by its parts.
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.
vertex
face
base
edge
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CONFIDENTIAL 30
Review
Examples of 3-dimensional figure.
Cube
A cube has 6 faces, 12 edges, 8 vertices
Cylinder
2 circular bases
Triangular pyramid
Triangular pyramid has 4 faces, 6 edges, 4 vertices
Rectangular pyramid
Triangular pyramid has 4 faces, 12 edges, 8
vertices
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CONFIDENTIAL 31
Review
Make a NetYou can make a net for any solid figure.
Net for a square pyramid.
CubeTriangular Prism
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CONFIDENTIAL 32
Review
Volume of a Cuboids
Cuboids are a 3-dimensional shape.
It has 3 different measurements.
Height
WidthDep
th
The volume of he cube is found using the formula
Volume = Height × Width × Depth
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CONFIDENTIAL 33
Review
The dimensions of a Rectangular prism is given.Find its volume.
Height = 6 cmWidth = 4 cmDepth = 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.
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CONFIDENTIAL 34
You have done a nice job.See you in the next session.