CONFIDENTIAL 1

2D vs. 3D (solid figures) and Volume

Grade 4

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

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) .

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

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

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

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

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

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

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

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

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.

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.

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)

CONFIDENTIAL 15

Name Sides Shape

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Names of Polygons

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

CONFIDENTIAL 17

Examples of 3-dimensional figure.

Cube

A cube has 6 faces, 12 edges, 8 vertices

Cylinder

2 circular bases

CONFIDENTIAL 18

Triangular pyramid

Triangular pyramid has 4 faces, 6 edges, 4 vertices

Rectangular prism

Rectangular prism has 4 faces, 12 edges, 8

vertices

CONFIDENTIAL 19

Make a NetYou can make a net for any solid figure.

Net for a square pyramid.

CubeTriangular Prism

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

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.

CONFIDENTIAL 22

BREAK

CONFIDENTIAL 23

Title: Format: WebEx Web BrowserDouble-click to edit

CONFIDENTIAL 24

Assignments

Identify 3-dimensional figure.Tell how many faces, edges and vertices it has

1) 2)

3) 4)

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

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.

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.

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

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

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

CONFIDENTIAL 31

Review

Make a NetYou can make a net for any solid figure.

Net for a square pyramid.

CubeTriangular Prism

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

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.

CONFIDENTIAL 34

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