= 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
![Page 1: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/1.jpg)
= 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
![Page 2: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/2.jpg)
= 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
![Page 3: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/3.jpg)
= 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
![Page 4: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/4.jpg)
Volume = 24 centimetre cube
One unit of Volume is the “CUBIC CENTIMETRE”
2cm
3cm
4cm
= 24 cm³
Volumes by Counting Cubes
![Page 5: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/5.jpg)
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
![Page 6: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/6.jpg)
Volume = l x b x hV = 18 x 5 x 27V = 2430 cm³
Example 1
18 cm5 cm
27cmHeilander’sPorridge Oats
Working
![Page 7: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/7.jpg)
Example 2
2cm
Volume = l x b x hV = 2 x 2 x 2V = 8 cm³
Working
![Page 8: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/8.jpg)
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
![Page 9: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/9.jpg)
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
![Page 10: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/10.jpg)
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
![Page 11: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/11.jpg)
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
![Page 12: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/12.jpg)
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
![Page 13: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/13.jpg)
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
![Page 14: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/14.jpg)
Face Edges and Vertices
Faces are squares
Calculate the number of faces
edges and vertices for a cube.
6 faces12 edges8 vertices
![Page 15: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/15.jpg)
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
![Page 16: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/16.jpg)
Surface Area of the Cuboid
What is meant by the term surface area?
The complete area of a 3D shape
![Page 17: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/17.jpg)
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
![Page 18: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/18.jpg)
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
![Page 19: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/19.jpg)
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
![Page 20: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/20.jpg)
20
Any Triangle Area
h
b
Sometimes called the altitude
h = vertical height
![Page 21: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/21.jpg)
Any Triangle Area
6cm
8cm
Example 1 : Find the area of the triangle.
Area = 24cm²
![Page 22: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/22.jpg)
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
![Page 23: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/23.jpg)
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
![Page 24: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/24.jpg)
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
![Page 25: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/25.jpg)
= 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
![Page 26: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/26.jpg)
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
![Page 27: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/27.jpg)
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
![Page 28: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/28.jpg)
V = πr2h
Example : Find the volume of the cylinder below.
= π(5)2x10
5cm
Cylinder(circular Prism)
10cm
= 250π cm
Volume of a Cylinder
![Page 29: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/29.jpg)
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
![Page 30: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/30.jpg)
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
![Page 31: = 1 centimetre cube](https://reader036.vdocuments.site/reader036/viewer/2022062310/568156d6550346895dc4720b/html5/thumbnails/31.jpg)
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