Form 3

1
Cone and Pyramid
Title
Subject
Mathematics
Target Audience
Form 3
Usage
Lecturing
2
Prerequisite knowledge
1. Pythagoras Theorem.
2. Area of some plane figures e.g. square,
rectangle, triangle, circle, sector
3. Ratio and proportion
Objectives
Let the students know and apply the mensuration
concepts
3
Egyptian Pyramid
4
These are pyramids
5
Slant edges
6
cube
Three congruent pyramids
7

For any pyramid,
8
Solution
VF2 (152 - 92 ) cm2
12 cm
Volume of the pyramid
768 cm3
9
? Pyramid B
? A frustum
-

10
Solution
Volume of VEFGH
128 cm3
Volume of VABCD
1024 cm3
Volume of frustum ABCDEFGH
(1024 - 128 ) cm3
896 cm3
11
(No Transcript)
12
Total surface area of pyramid VABCD
lateral faces
Base
13
Solution
Total surface area of pyramid VABCD
Area of ABCD
(Area ?VAB Area ?VDC Area ?VBC Area
?VAD )
Area of ABCD
(Area ?VAB ? 2) (Area ?VBC ? 2)
48 cm2
( (40 ? 2) (30 ? 2)) cm2
188 cm2
14
How to generate a cone?
...
...
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How to calculate the curved surface area ?
Cut here
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Curved surface area
After cutting the cone,
Curved surface area Area of the sector
?Curved surface area 1/2 ( l ) ( 2p r )
p r l
?Curved surface area pr l
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Volume of a cone
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How to calculate total surface area of a cone?

Total surface area pr2 pr l
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Examples

• 1 a)

20
b) what is the total surface area?
p52
Based Area
25pcm2
Slant height
13 cm
Curved surface area
p(5) ( 13)
65p cm2
Total surface area
based area curved surface area
25p65p 90p
282.6cm2 (corr.to 1 dec.place)
21
Volume of Frustum
22
Volume of Frustum
Volume of frustum volume of big cone - volume
of small cone
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Exercises
Start Now
Exit
24
Q1
The volume of a pyramid of square base is 96 cm3.
If its height is 8 cm, what is the length of a
side of the base?
Answer
Help
To Q2
25
Q2
In the figure, the volumes of the cone AXY and
ABC are 16 cm3 and 54 cm3 respectively, AX XB
Answer
Help
To Q3
26
Q3
In the figure, VABCD is a right pyramid with a
rectangular base. If AB18cm, BC24cm and
CV25cm, find
a) the height (VM) of the pyramid, b)
volume of the pyramid.
Answer
Help
To Q4
27
Q4
The figures shows a right circular cone ABC. If
AD 48cm and AC 50cm, find
Help
28
Answer for Q1
Let V is the volume of the pyramid and y be the
length of a side of base
what is the length of a side of the base?
288 8y2
Back to Q1
36 y2
y 6
To Q2
Therefore, the length of a side of base is 6 cm
29
Answer for Q2
Hints Using the concept of RATIOS
AX XB ?
A
?AB AX XB and AX 2, AB 3
Back to Q2
?3 2 XB
?XB 1
Therefore, AX XB 2 1
To Q3
30
a) the height (VM) of the pyramid
b) volume of the pyramid.
AC2 182 242
Volume of the pyramid is
AC2 900
AC 30cm
Answer for Q3
252 VM2 MC2
2880cm3
625 VM2 152
Therefore, the volume of the pyramid is 2880cm3
625 - 225 VM2
VM2 400
Back to Q3
VM 20cm
Therefore, the height (VM) of the pyramid is 20 cm
To Q4
31
Answer for Q4
(a) the base radius (r)
(b) the volume of the cone
The volume (V) of cone is
The radius is r, therefore
502 482 r2
2500 2304 r2
196 r2
704 cm3
r 14
The volume is 704 cm3
A
The radius is 14cm.
(Take ? 22/7)
Back to Q4
32
End of lesson!