 Volumes by Counting Cubes

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Volumes by Counting Cubes
Volume is the amount of space a 3D - shape takes up 1cm 1cm 1cm One Unit of Volume is the “CUBIC CENTIMETRE” = 1 centimetre cube = 1 cm³

Volumes by Counting Cubes
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³? 1cm 1cm 1cm 1cm = 2 centimetre cubes = 2 cm³

Volumes by Counting Cubes
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³ 1cm 1cm 1cm = 3 centimetre cubes = 3 cm³

Volumes by Counting Cubes
One unit of Volume is the “CUBIC CENTIMETRE” 3cm 2cm 4cm Volume = 24 centimetre cube = 24 cm³

A short cut ! Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth
height Area of rectangle breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height

Example 1 27cm 5 cm 18 cm Working Volume = l x b x h V = 18 x 5 x 27
Heilander’s Porridge Oats V = 18 x 5 x 27 V = cm³ 27cm 5 cm 18 cm

Example 2 Working Volume = l x b x h V = 2 x 2 x 2 V = 8 cm³ 2cm

Liquid Volume Volume = l x b x h = 1 cm³
I’m a very small duck! How much water does this hold? 1 cm 1 cm 1 cm Volume = l x b x h = 1 cm³ A cube with volume 1cm³ holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre.

Example 1 Working Volume = l x b x h V = 6 x 3 x 12 V = 216 cm³
Liquid Volume Working Orange Flavour Volume = l x b x h V = 6 x 3 x 12 12 cm V = 216 cm³ = 216 ml 3 cm 6 cm So the carton can hold 216 ml of orange juice. How much juice can this carton hold? Remember: 1 cm³ = 1 ml

Example 2 Working Volume = l x b x h V = 100 x 30 x 50 V = 150 000 cm³
Liquid Volume Working Volume = l x b x h V = 100 x 30 x 50 V = cm³ 50 cm = ml = 150 litres 30 cm 100 cm How much water can this fish tank hold in litres? 1cm3 = 1 ml 1000 ml = 1 litre So the fish tank can hold 150 litres of water.

Revision of Area The Square The Rectangle The RAT b h l b l l

Face Edges and Vertices
Don’t forget the faces edges and corners we can’t see at the back Face Edges and Vertices The shape below is called a cuboid. It is made up of FACES, EDGES and VERTICES. Edges are where the two faces meet (lines) Faces are the sides of a shape (surface area) Vertices where lines meet (corners)

Face Edges and Vertices
Calculate the number of faces edges and vertices for a cuboid. Face Edges and Vertices 6 faces 12 edges Front and back are the same 8 vertices Top and bottom are the same Right and left are the same

Face Edges and Vertices
Calculate the number of faces edges and vertices for a cube. Face Edges and Vertices 6 faces 12 edges Faces are squares 8 vertices

Face Edges and Vertices
Calculate the number of faces, edges and vertices for these shapes Face Edges and Vertices 5 faces 9 edges 6 Vertices 2 faces 1 edges 1 Vertices Cone Triangular Prism Cylinder Sphere 3 faces 2 edges 1 faces 0 Vertices 0 edges 0 Vertices

Surface Area of the Cuboid
What is meant by the term surface area? The complete area of a 3D shape

Find the surface area of the cuboid
Example Find the surface area of the cuboid Working Front Area = l x b = 5 x 4 =20cm2 Top Area = l x b = 5 x 3 =15cm2 4cm Side Area = l x b = 3 x 4 =12cm2 3cm 5cm Total Area = = 94cm2 Front and back are the same Top and bottom are the same Right and left are the same

Find the surface area of the cuboid
Example Find the surface area of the cuboid Working Front Area = l x b = 8 x 6 =48cm2 Top Area = l x b = 8 x 5 =40cm2 6cm Side Area = l x b = 6 x 5 =30cm2 5cm 8cm Total Area = = 236cm2 Front and back are the same Top and bottom are the same Right and left are the same

Volume of Solids Definition : A prism is a solid shape with
uniform cross-section Hexagonal Prism Cylinder (circular Prism) Triangular Prism Pentagonal Prism Volume = Area of Face x length

Sometimes called the altitude
Any Triangle Area h = vertical height Sometimes called the altitude h b 20

Any Triangle Area Example 1 : Find the area of the triangle. 6cm
Area = 24cm²

Volume of Solids Definition : A prism is a solid shape with
uniform cross-section Q. Find the volume the triangular prism. Triangular Prism Volume = Area of face x length = 20 x 10 = 200 cm3 10cm 20cm2

Volume of a Triangular Prism
Working Triangle Area = = 2 x4 = 8 cm2 4cm Volume = Area x length = 8 x 10 = 80cm3 10cm 4cm Find the volume of the triangular prism

Find the volume of the triangular prism.
Example Find the volume of the triangular prism. Working Triangle Area = = 3 x 3 = 9 cm2 Volume = Area x length = 9 x 30 = 270cm3 6cm 3cm 30cm Total Area = = 132cm2

Find the surface area of the right angle prism
Example Find the surface area of the right angle prism Working Triangle Area = = 2 x3 =6cm2 Rectangle 1 Area = l x b = 3 x10 =30cm2 4cm 5cm Rectangle 2 Area = l x b 3cm 10cm = 4 x 10 =40cm2 Rectangle 3 Area = l x b 2 triangles the same = 5 x 10 =50cm2 1 rectangle 3cm by 10cm Total Area = = 132cm2 1 rectangle 4cm by 10cm 1 rectangle 5cm by 10cm

Surface Areaof a Triangular Prism
Working Triangle Area = = 2 x4 = 8 cm2 5cm Rectangle 1 Area = l x b 4cm = 5 x10 =50cm2 10cm Rectangle 2 Area = l x b 4cm = 5 x10 =50cm2 2 triangles the same Rectangle 3 Area = l x b 2 rectangle the same 5cm by 10cm = 4 x 10 =40cm2 1 rectangle 4cm by 10cm Total Area = = 156cm2

Volume of a Cylinder Volume = Area x height = πr2 = πr2h h x h
The volume of a cylinder can be thought as being a pile of circles laid on top of each other. Volume = Area x height h = πr2 x h Cylinder (circular Prism) = πr2h

Volume of a Cylinder V = πr2h = π(5)2x10 = 250π cm
Example : Find the volume of the cylinder below. 5cm Cylinder (circular Prism) 10cm V = πr2h = π(5)2x10 = 250π cm

Surface Area of a Cylinder 2πr h Total Surface Area = 2πr2 + 2πrh
The surface area of a cylinder is made up of 2 basic shapes can you name them. Cylinder (circular Prism) 2πr Curved Area =2πrh Top Area =πr2 Roll out curve side  h Bottom Area =πr2 2 x Circles Rectangle Total Surface Area = 2πr2 + 2πrh

Surface Area of a Cylinder = (2 x π x 3²) + (2 x π x 3 x 10)
Example : Find the surface area of the cylinder below: 3cm Surface Area = 2πr2 + 2πrh 10cm = (2 x π x 3²) + (2 x π x 3 x 10) = 2 x π x x π x 30 Cylinder (circular Prism) = cm²

Surface Area of a Cylinder = 2 x π x 3 x 9 = 169.64 cm2
Radius = 1diameter 2 Example : A net of a cylinder is given below. Find the curved surface area only! 6cm Curved Surface Area = 2πrh = 2 x π x 3 x 9 9cm = cm2