CLASS:� JSS 1
TERM: 3rd TERM
TOPIC: 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
Net of cuboid�
A cuboid has the following properties:
Cylinders and Prisms
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
General Evaluation/Revision Questions
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