= 1 centimetre cube
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
= 1 centimetre cube
1cm 1cm
1cm
= 1 cm³
One Unit of Volume is the “CUBIC CENTIMETRE”
Volume is the amount of space a 3D - shape takes up
Volumes by Counting Cubes
= 2 centimetre cubes
1cm
1cm
1cm
= 2 cm³
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³?
1cm
Volumes by Counting Cubes
= 3 centimetre cubes
= 3 cm³
This shape is made up of 1 centimetre cubes placed next to each other. What is its volume
in cm³
1cm
1cm
1cm
1cm
Volumes by Counting Cubes
Volume = 24 centimetre cube
One unit of Volume is the “CUBIC CENTIMETRE”
2cm
3cm
4cm
= 24 cm³
Volumes by Counting Cubes
A short cut !
6 = 72 cm³ Volume =
length
x breadth x 4
x height
length
breadth
height
x 3 Volume =
3cm
4cm
6cmArea of rectangl
e
Volume = l x b x hV = 18 x 5 x 27V = 2430 cm³
Example 1
18 cm5 cm
27cmHeilander’sPorridge Oats
Working
Example 2
2cm
Volume = l x b x hV = 2 x 2 x 2V = 8 cm³
Working
1 cm
1 cm1 cm
Volume = = 1 cm³ x h x b l
How much water does this hold?
A cube with volume 1cm³ holds exact 1 millilitre of liquid.A volume of 1000 ml = 1 litre.
I’m a very small duck!
Liquid Volume
Example 1
12 cm
6 cm3 cm
OrangeFlavour
Volume = l x b x hV = 6 x 3 x 12V = 216 cm³
= 216 ml
So the carton can hold 216 ml of orange juice.
How much juice canthis carton hold? Remember:
1 cm³ = 1 ml
WorkingLiquid Volume
Example 2
50 cm
100 cm30 cm
Volume = l x b x hV = 100 x 30 x 50V = 150 000 cm³
= 150 000 ml
So the fish tank can hold 150 litres of water.
How much water can this fish tank hold in litres?
1cm3 = 1 ml1000 ml = 1
litre
= 150 litres
WorkingLiquid Volume
Revision of Area
2Area l l l 12Area b h
l
l Area l b
l
b h
b
The Square The Rectangle The RAT
Face Edges and Vertices
The shape below is called a cuboid.It is made up of FACES, EDGES and VERTICES.
Faces are the sides of a shape(surface area)
Edges are where the two
faces meet (lines)
Vertices where lines meet (corners)
Don’t forget the faces edges and corners we can’t see at the back
Face Edges and Vertices
Front and back are the sameTop and bottom are the sameRight and left are the same
Calculate the number of faces
edges and vertices for a cuboid.
6 faces12 edges8 vertices
Face Edges and Vertices
Faces are squares
Calculate the number of faces
edges and vertices for a cube.
6 faces12 edges8 vertices
Face Edges and Vertices
Calculate the number of faces,
edges and vertices for these shapes
CylinderCone
Sphere
Triangular Prism
3 faces2 edges
0 Vertices
5 faces9 edges
6 Vertices 2 faces1 edges
1 Vertices
1 faces0 edges
0 Vertices
Surface Area of the Cuboid
What is meant by the term surface area?
The complete area of a 3D shape
Front Area = l x b= 5 x 4 =20cm2
Example Find the surface
area of the cuboid
Working
5cm
4cm
3cm
Top Area = l x b= 5 x 3 =15cm2
Side Area = l x b= 3 x 4 =12cm2
Total Area
= 20+20+15+15+12+12= 94cm2
Front and back are the sameTop and bottom are the sameRight and left are the same
Front Area = l x b= 8 x 6 =48cm2
Example Find the surface
area of the cuboid
Working
8cm
6cm
5cm
Top Area = l x b= 8 x 5 =40cm2
Side Area = l x b= 6 x 5 =30cm2
Total Area
= 48+48+40+40+30+30= 236cm2
Front and back are the sameTop and bottom are the sameRight and left are the same
Definition : A prism is a solid shape with uniform cross-section
Cylinder(circular Prism) Pentagonal PrismTriangular Prism
Hexagonal Prism
Volume = Area of Face x length
Volume of Solids
20
Any Triangle Area
h
b
Sometimes called the altitude
h = vertical height
Any Triangle Area
6cm
8cm
Example 1 : Find the area of the triangle.
Area = 24cm²
Definition : A prism is a solid shape with uniform cross-section
Triangular PrismVolume = Area of face x length
Q. Find the volume the triangular prism.
20cm210cm= 20 x 10 = 200 cm3
Volume of Solids
Volume of a Triangular Prism
4cm
4cm10cm
= 2 x4 = 8 cm2
Working
Volume = Area x length = 8 x 10 = 80cm3
Triangle Area = 1bh2
Find the volume of the triangular prism
Example Find the volume of
the triangular prism.
Total Area = 6+6+30+40+50 = 132cm2
3cm
6cm30cm
= 3 x 3 = 9 cm2
Working
Volume = Area x length = 9 x 30 = 270cm3
Triangle Area = 1bh2
= 2 x3 =6cm2
Example Find the surface area of the right
angle prism
Working
Rectangle 1 Area = l x b= 3 x10 =30cm2
Rectangle 2 Area = l x b= 4 x 10 =40cm2
Total Area = 6+6+30+40+50 = 132cm2
2 triangles the same1 rectangle 3cm by 10cm1 rectangle 4cm by 10cm
3cm
4cm10cm
1 rectangle 5cm by 10cm
Triangle Area = 1bh2
Rectangle 3 Area = l x b= 5 x 10 =50cm2
5cm
Surface Areaof a Triangular Prism
4cm
4cm10cm
= 2 x4 = 8 cm2
WorkingTriangle Area = 1bh2
2 triangles the same2 rectangle the same 5cm by 10cm1 rectangle 4cm by 10cm
5cmRectangle 1 Area = l x b
= 5 x10 =50cm2
Rectangle 3 Area = l x b= 4 x 10 =40cm2
Total Area = 8+8+50+50+40 = 156cm2
Rectangle 2 Area = l x b= 5 x10 =50cm2
Volume = Area x height
The volume of a cylinder can be thought as being a pile
of circles laid on top of each other.
= πr2
Volume of a Cylinder
Cylinder(circular Prism)
x hh
= πr2h
V = πr2h
Example : Find the volume of the cylinder below.
= π(5)2x10
5cm
Cylinder(circular Prism)
10cm
= 250π cm
Volume of a Cylinder
Total Surface Area = 2πr2 + 2πrh
The surface area of a cylinder is made up of 2 basic shapes can you name them.
Curved Area =2πrhCylinder(circular Prism)
h
Surface Area of a Cylinder
Roll out curve side
2πrTop Area =πr2
Bottom Area =πr2
Rectangle
2 x Circles
Example : Find the surface area of the cylinder below:
= (2 x π x 3²) + (2 x π x 3 x 10)
3cm
Cylinder(circular Prism)
10cm
= 2 x π x 9 + 2 x π x 30
Surface Area of a Cylinder
Surface Area = 2πr2 + 2πrh
= 245.04cm²
Example : A net of a cylinder is given below.Find the curved surface area only!
Surface Area of a Cylinder
9cm
Radius = 1diameter
2
Curved Surface Area = 2πrh6cm
= 2 x π x 3 x 9= 169.64 cm2