Subject : MATHEMATICS
Class : JSS 1
Term :THIRD TERM
Week : WEEK FIVE
- Scheme of Work
- Online Information
- 9 Year Basic Education Curriculum
Previous Knowledge :
The pupils have previous knowledge of
Perimeter of regular polygon
Behavioural Objectives : At the end of the lesson, the pupils should be able to
- define Three dimensional ( 3-D) shapes
- give examples of Three dimensional ( 3-D) shapes
- calculate the volume of Three dimensional ( 3-D) shapes
THREE DIMENSIONAL SHAPES
Three dimensional ( 3-D) shapes are also called solid shapes. They have length, breadth and height unlike 2-D shapes that have only length and breadth. Examples of 3-D shapes are cubes, cuboids, cylinders, prisms, pyramids and spheres. They are also called geometrical solids.
Face: a surface of solid shape
Edge: a line on a solid where two faces meet
Vertex (plural vertices): a point or corner on a solid, usually where edges meet
Net: a flat shape that you can fold to make a solid
Cuboids and Cubes
A cube has the following properties
- It has 12 straight edges
- It has 8 vertices
- It has 6 square faces
- Its net consist of 6 square faces joined together
Net of cuboid
A cuboid has the following properties:
- It has 12 straight edges
- It has 8 vertices
- It also has 6 rectangular faces
- Its net consist of 6 rectangular faces
Cylinders and Prisms
- A cylinder has two circular faces
- It has 1 curved surface
- It has 2 curved edges
- Its net consists of two circular faces and 1 rectangular face i.e. its net consist of 2 circles and 1 rectangle.
The net of a cylinder has two circles and one rectangle
The base and top faces of a prism are always the same shape. The names of prisms come from the shape of their base and top faces.
Triangular Prism Hexagonal prism
Cones and pyramids
A cone is a solid shape with curved body, circular base and a pointed end.
A pyramid is a solid shape with a flat base and triangular faces rising to meet at a common point called its vertex. There are many types of pyramid. The different types are named after the shapes of the bases they have:
Rectangle pyramid Trapezoid Pyramid
A sphere is a solid shape with perfectly round surface. Examples are orange, ball, shotput, etc.
Volumes of Solids
Volume of Cuboids
The volume of solids is a measure of the amount of space it occupies. A solid object is also called a 3-dimensional ( 3-D) object. The cube is used as the basic shape to estimate the volume of solid. Therefore, volume is measured in cubic unit. A cube of an edge 1cm has a volume of one cubic centimetre (1cm3).
The volume of a cuboid is given by:
Volume= length x width x height i.e. V = l x w x h
In the above formula, A = l x w where A= base area of the cuboid
Hence: Volume of a cuboid = base area x height
V = A x h
Volumes of cubes
When all the edges of a cuboid are equal, it is called a cube. If one edge is l unit long, then
Volume of a cube = length x height x width
i.e V = l×l×l
A cube of an edge 3cm will have a volume of 3 x 3 x 3 = 27cm3.
The above formula can be used to find the edge of a cube when the volume is given.
l3 = V
l = 3V
Calculate the volume of a rectangular tank with dimensions 20cm by 15cm by 12 cm.
Volume = length x width x height
V = l x w x h
= (20 x 15 x 12) cm3
A cuboid, 12 cm long and 8cm wide has a volume of 624cm3. Find the height of the cuboid.
V = 624cm3
Substituting V = 624cm3, l = 12cm, and w = 8cm
Length x width x height = volume
L x w x h = V
12 x 8 x h = 624
96h = 624
Divide both sides by 96, h = 62496 = 6.5cm
The height of the cuboid = 6.5cm
A tank of water in the shape of a cuboid has a square base. If the depth of water in the tank is 3m high and the volume of the water inside the cuboid is 243m2. Calculate the width of the tank.
Volume of a cuboid= base area x height
Since it has a square base, the base area = l2 , i.e. l = w.
243m3 = l2 x 3m
l2= 243m23cm = 81m2
Therefore, l = 281 = 9m
The width of the tank is 9m
The topic is presented step by step
The class teacher revises the previous topics
He introduces the new topic
The class teacher allows the pupils to give their own examples and he corrects them when the needs arise
- A cube volume of a cube is given as 512cm3
- What is the length of one edge of the cube?
- How many small cubes of edge 2cm can be placed together to make this cube?
- A cuboid has a base area of 35cm2 and a height of 3.5cm. What is the volume of the cuboid?
General Evaluation/Revision Questions
- A rectangular prism ( cuboid) has a volume of 680cm3 and its height is 20cm. What is the area of the base of the prism?
- The base of a swimming pool is 192m2. The depth of the swimming pool is 1.8m. find the volume of water the swimming pool can hold.
- A book measures 18cm by 12cm by 3cm. Calculate its volume
- What is the volume of a cube of edge 5cm. (a) 15cm3 (b) 75cm3 (c) 125cm3 (d) 25cm3
- Find the volume of air in a container whose dimensions are: length = 25cm, width = 20cm and height= 10cm (a) 5000cm3 (b) 2500cm3 (c) 4500cm3 (d) 500cm3
- The volume of a cube is given as 512cm3. What is the length of one edge of the cube? (a) 10cm (b) 6cm (c) 4cm (d) 8cm
- How many small cubes of edge 2cm can be placed together to make the cube in question 3 above? (a) 66 (b) 32 (c) 64 (d) 128
- Calculate the volume of a cuboid with dimension 18cm by 12cm by 8cm. (a) 1728cm3 (b) 512cm3 (c) 144cm3 (d) 1872cm3
- The base of a cuboid has one side equal to 10cm, and the other side is 5cm longer. If the height of the cuboid is 7cm, find the volume of the cuboid.
- A cuboid measures xcm by 3xcm by 5xcm
- Work out the volume of the cuboid in terms of x
- What is the volume of the cuboid if x = 10cm?
The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and where the needs arise.
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