surface area 3d shapes. square pyramid triangular prism square prism rectangular prism rectangular...
TRANSCRIPT
Surface Area
3D shapes
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Instructions for use
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Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
3 easy steps to calculate the Surface Area of a solid figure
1. Determine the number of surfaces and
the shape of the surfaces of the solid
2. Apply the relevant formula for the area of
each surface
3. Sum the areas of each surface
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Surface Area – Basic concept
Determine the number and shape
of the surfaces
that make up the solid.
It might be easier to think of the net of the solid.
square rectanglerectangle square
rectangle
rectangle
4 rectangular faces and 2 square
faces
When you’ve done all that find the area of each face and then find the total of the areas.
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Square prism
18 cm
2410
904252
1854552
cmA
A
A
Two square faces
Find the surface area of this figure with square base 5 cm and height 18 cm
5 cm
Four rectangular faces
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Rectangular prism
5 cm
15 cm
20 cm
155A
155A
205A
205A2015A 2015A
2950
30021002752
2015220521552
cmA
A
A
Now sum
these areas
Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm.
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Triangular Prism
12 cm
20 cm10 cm
8122
1A
2010A 2010A 2012A
2736
24040096
2012201028122
12
cmA
A
A
Hence, total surface area
8122
1A
Find the surface area of this figure with dimensions as marked.
12 cm
10 cm
6
8
Use Pythagoras’ theorem to find the height of
the triangle!
Determine the number of faces and the shape of
each face
Apply the area
formulae for each face
Sum the areas to give
the total surface area
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Square Pyramid
10 cm
P
Q
13102
1A 1310
2
1A 1310
2
1A 1310
2
1A
1010A
Find the surface area of this figure with square base 10 cm and height 12 cm.
4 triangular faces with the same
dimensions and 1 square face
We need to find the height of each triangular
face.
12
10 cm
P
Q 5
R
T
10
Use Pythagoras’ theorem to find the height of the triangular
face.13
10
13
TR
P
Each triangular face will have base 10 cm and height 13 cm.
12
2360
100260
101013102
14
cmA
A
A
Hence, total surface area
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Rectangular Pyramid
10 cm
P
Q 12 cm
8 cmR
ST
V
5
8
6
8
5 faces altogether:
2 pairs of congruent triangular faces
1 rectangular face
2333
2208912
121010108912
101210102
128912
2
12
cmA
A
A
A
Hence, total surface area
10
68 22
h
h
10
10
First find the unknown heights using
Pythagoras’ theorem89
58 22
h
h
89
12
Find the surface area of this figure with dimensions as marked.
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
CylinderFind the surface area of this cylinder with height 25 cm and diameter 20 cm.
Required formula: rhrA 22 2
20
25 cmCurved surface
Curved surface
h
r2
Think of the net of the cylinder to understand the formula.
2
2
2
700
500200
25102102
22
cmA
A
A
rhrA
Hence, total surface area
210A
210A
25102 A
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
ConeFind the surface area of this cone of height 15 cm radius 5 cm.
lrrA 2Required formula
l refers to the slant
height
Total surface area:
2
2
9.326
102525
10555
cmA
A
A
5
15l
105
250
515 22
l
l
l
Use Pythagoras’ theorem
Now sum these areas
l
Consider the net of the cone
Now calculate the areas. 1055A
25A
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
SphereFind the surface area of this sphere with diameter 5 cm.
24 rA Required formula
Easy! The sphere is one continuous surface so just
substitute into the formula 2
2
2
5.78
2
54
4
cmA
A
rA
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
Hemisphere
A hemisphere is a half
sphere. But we need to add in
the area of the circular
base.
Find the surface area of this hemisphere with diameter 5 cm.
22 rA Required formula 2rA
2rA
22 rA Total surface area:
2
2
2
22
9.58
2
53
3
2
cmA
A
rA
rrA
Square Pyramid
Triangular Prism
Square Prism
Rectangular Prism
Rectangular Pyramid
Basic
rulesBasic
concept
Cylinder
Cone
Sphere
Hemisphere
© Rosemary Vellar
Excel challenge
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