© T Madas. In 2 dimensions square rectangle In 3 dimensions cube cuboid.
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Transcript of © T Madas. In 2 dimensions square rectangle In 3 dimensions cube cuboid.
© T Madas
© T Madas
In 2 dimensions
square
rectangle
In 3 dimensions
cube
cuboid
© T Madas
Face
FaceEdge
Vertex
Vertex
© T Madas
1cm
What is the surface area of a solid shape?
Surface Area is the total area of all of its faces
4
3
12
x 2 =
x 2 =
x 2 =
8
6
24
38cm2
© T Madas
What is the surface area of a solid shape?
Surface Area is the total area of all of its faces
5 x 3= 15
6 x 3= 18
5 x 6= 30
x 2 =
x 2 =
x 2 =
30
36
60
1261 m
m2
© T Madas
Calculatingthe Surface Area
of a Cuboid
© T Madas
20 cm
15 cm
10 c
m
The amount of card needed for a box
20 x 10= 200
15 x 10= 15020 x 15
= 300
x 2 =
x 2 =x 2 =
400300600
F/B:
L/R:
T/B:
© T Madas
20 cm
15 cm
SURFACE AREA for this box
20 x 10= 200
15 x 10= 15020 x 15
= 300
x 2 =
x 2 =x 2 =
400300600
1300cm2
The amount of card needed for a box
F/B:
L/R:
T/B:
10 c
m
© T Madas
Calculatingthe Surface Area
of a Cuboid
© T Madas
2 m
5 m
8 m
SURFACE AREA for this cuboid
5 x 2= 10
8 x 2= 168 x 5= 40
x 2 =
x 2 =x 2 =
20
3280
132 m2
F/B:
L/R:
T/B:
© T Madas
Calculatingthe Surface Area
of a Cube
© T Madas
2 m
2 m2 m
SURFACE AREAfor this cube
2 x 2= 4x 6 = 24m2
© T Madas
Surface Area & Volume Practice
© T Madas
Each little cube has side equal to 1 cm
Volume =Surface Area =
1 cm3
6 cm2
© T Madas
Each little cube has side equal to 1 cm
2 cm3
10 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
4 cm3
16 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
6 cm3
22 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
8 cm3
24 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
12 cm3
40 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
12 cm3
32 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
16 cm3
48 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
12 cm3
36 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
16 cm3
40 cm2
Volume =Surface Area =
© T Madas
Each little cube has side equal to 1 cm
27 cm3
54 cm2
Volume =Surface Area =
© T Madas
© T Madas
The nets shown below belong to two cuboids.The squares on this grid are 1 cm apart.1. Calculate the surface area of each cuboid.2. Show that both cuboids have the same volume.
12
12
12
12
16 16
Surface Area =80cm2
24
6
24
6
16 16
Surface Area =
92cm2
© T Madas
The nets shown below belong to two cuboids.The squares on this grid are 1 cm apart.1. Calculate the surface area of each cuboid.2. Show that both cuboids have the same volume.
Volume =
= 48cm3
3 x 4
w x l x h= 3x 4x 4
Volume =
= 48cm3
w x l x h= 3x 8x 2
3 x 8
© T Madas
© T Madas
Four models made of unit cubes are shown below.
All models have a volume of 5 cm3.
Which pairs of models have the same surface area?
5 x 2=105 x 2=101 x 2= 2
22 cm2
4 x 2= 83 x 2= 63 x 2= 6
20 cm2
3 x 2= 64 x 2= 84 x 2= 8
22 cm2
5 x 2=102 x 2= 43 x 2= 6
20 cm2
© T Madas
Four models made of unit cubes are shown below.
All models have a volume of 5 cm3.
Which pairs of models have the same surface area?
22 cm2 20 cm2
22 cm2
20 cm2
© T Madas
© T Madas
5080
A winners podium is made by stacking 6 identical cuboids as shown below, each measuring 80 cm by 50 cm by 20 cm.
The outside of the podium is to be painted, except the part touching the ground.
What is the surface area to be painted?
20
Measurements in cm
80x20 19200 cm2=1600 cm2 x12=
80x50 12000 cm2=4000 cm2 x 3=
50x20 6000 cm2=1000 cm2 x 6=
The surface area to be painted is 37200 cm2
© T Madas
© T Madas
5 cm
13 cm
A cuboid is made by stacking 1 cm cubes, as shown in the diagram.
The cuboid is painted yellow on all of its six faces.
How many cubes will have paint on one face only?
9 c
m
Cubes making up the edges of the cuboid will have 2 or 3 faces painted.
Painted cubes which do not form the edges of the cuboid will have only one face painted.
© T Madas
5 cm
13 cm
A cuboid is made by stacking 1 cm cubes, as shown in the diagram.
The cuboid is painted yellow on all of its six faces.
How many cubes will have paint on one face only?
9 c
m
11 x 3 66 cubes= 33 x 2 =
7 x 3 42 cubes= 21 x 2 =
12 x 8 192 cubes= 96 x 2 =
300
© T Madas
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces.
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
24
24
8
TOTAL
no red face
1 red face
2 red faces
3 red faces
© T Madas
A cube is made up by connecting 4 rows by 4 columns by 4 layers of unit cubes.The larger cube is then painted red on the outside of all of its 6 faces. How many of the unit cubes have 3 red faces, 2 red faces, 1 red face and no red faces.
TOTAL
8
64
24
24
8
no red face
1 red face
2 red faces
3 red faces
© T Madas
