Volume and Surface Area of Pyramids. 2nd Grade of Secondary School
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Volume and Surface Area of Pyramids for 2nd grade of secondary school for Singapore Curriculum. The learning material resources for media taken from New Syllabus Mathematics book (7ed), published by Shinglee.

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Slide 1  Mathematics
 Volume and Surface Area of Pyramids
 2nd grade of Secondary School
 By: I Putu Eka Prana Yoga

Slide 2  Calculate the volume and the surface area of pyramids.
 Solve problems involving the volume and the surface area of composite solids made up of pyramids.
 Learning Objectives

Slide 3  Learning Agenda
 Classroom Discussion
 Types of Pyramids
 Volume and Surface of Pyramids
 Exercise

Slide 4  What are Pyramids?
 The Great Pyramids
 Tetrahedral Dice
 Louvre Pyramid
 Rice Dumpling
 Can you identify some common features of these pyramids?
 What do you notice about the slanted faces of these pyramids?
 What do you notice about the bases of these pyramids?

Slide 5  Definition of a Pyramid
 A pyramid is a solid in which one of the faces is a polygonal base and the other slanted faces are triangles joined to the edges.

Slide 6  Types of Pyramids
 Triangular Pyramid
 ________ Pyramid
 _________ Pyramid
 Rectangular Pyramid

Slide 7  Volume of Pyramids
 Volume of Prism = area across section x height
 = base area x height

Slide 8  Investigation

Slide 9  Investigation
 Volume of Pyramids

Slide 10  Investigation
 Volume of Pyramids

Slide 11  Volume of Pyramids
 Volume of Pyramids =

Slide 12  Example:
 OABC is Triangular Pyramid with a base area of 25 cm2 and a height of 8 cm.
 Find the Volume of Triangular Pyramid
 O
 A
 B
 C

Slide 13  Exercise 1
 O
 C
 B
 A

Slide 14  Example:
 VPQRS is a rectangular pyramid where PQ = 30 m and QR = 20 m.
 Given that the Volume of the pyramid is 7000 m3, find its height?
 V
 30 m
 Q
 R
 S
 P
 20 m

Slide 15  Exercise 2
 V
 R
 Q
 P
 10 m
 6 m
 S
 O

Slide 16  Surface Area of Pyramids
 Total Surface area of Pyramid = Total area of all faces
 The net of square pyramid
 The square pyramid

Slide 17  Example:
 OPQRS is a pyramid with square base of length 14 cm. Given that the slant height
 of the pyramid is 17 cm, draw its net and hence, find its total surface area.
 O
 14 cm
 Q
 R
 P
 17 cm
 S

Slide 18  O
 14 cm
 Q
 R
 P
 17 cm
 S
 14 cm
 14 cm
 14 cm
 14 cm
 17 cm
 17 cm
 17 cm
 17 cm
 R
 S
 P
 Q
 O
 O
 O
 O

Slide 19  14 cm
 14 cm
 14 cm
 14 cm
 17 cm
 17 cm
 17 cm
 17 cm
 R
 S
 P
 Q
 O
 O
 O
 O

Slide 20  Exercise 3
 O
 Y
 X
 W
 A
 63 cm
 32 cm
 56 cm
 66 cm
 Z
 B

Slide 21  Example:
 A pyramid has a square base of length 10 cm and a total surface area of 272 cm2.
 Find the volume of the pyramid.
 10 cm
 V
 B
 C
 A
 D
 Q
 P
 Total Surface area of Pyramid =
 4 x area of triangular face
 + area of square base
 4 x area of triangular face
 4 x area of triangular face
 area of triangular face
 area of triangular face
 4 x area of triangular face

Slide 22  10 m
 V
 B
 C
 A
 D
 Q
 P

Slide 23  10 cm
 V
 B
 C
 A
 D
 Q
 P

Slide 24  10 m
 V
 B
 C
 A
 D
 Q
 P
 The volume of Pyramid =
 base area
 height

Slide 25  Quiz

Slide 26  Quiz 1
 C
 E
 F
 O
 D
 B
 A
 6 cm

Slide 27  Quiz 2
 O
 Z
 Y
 X
 7 m
 4 m
 5 m

Slide 28  Quiz 3

Slide 29  Quiz 4

Slide 30  Quiz 5
 V
 C
 B
 A
 16 cm
 9 cm
 15 cm
 D
 Q

Slide 31  Quiz 6
 V
 R
 Q
 P
 8 cm
 15 cm
 S

Slide 32  About This Learning Material
 This learning material is made by:
 I Putu Eka Prana Yoga
 iputueka1993@gmail.com
 @putupranayoga