# Lesson Notes By Weeks and Term - Junior Secondary School 3

GEOMETRY CONTD

SUBJECT: MATHEMATICS

CLASS:  JSS 3

DATE:

TERM: 2nd TERM

WEEK FOUR

TOPIC: GEOMETRY CONTD

Areas and Volumes of similar shaped

Scale Factor (Length Ratio)

P                  9cm              Q

A                          B

2                      6cm

D            3              C

S              R

Scale factor  =     9    or   6    =  3

3           2         1

Area factor   = (Scale factor)2

= (3/1)2        =   9/1     or   9.1

If the ratio of the length is X : Y

Then the ratio of the area is  X2 : Y2

Example 1:

In the diagram below, if the area of triangle ABC is 48cm2, find the area of triangle XYZ to 3s.f

A                X

550

650        600                      600

B     12cm         C         Y          4cm          Z

Solution

In âABC,

In âXYZ, 0

Since then corresponding angles are equal, âABC and âXYZ are similar

Scale factor  =     4     =       1

12    3

Area factor  = (1/3)2    = 1/9

Area of âXYZ     =     1

Area of âABC          9

Area of âXYZ     =     1

48          9

Area of âXYZ     =     48

9            =  5.333cm

Area of âXYZ  =  5.3 cm2    to 2 s.f.

Volume of Similar Shapes

Volume of factor = (Scale factor)3

If the ratio of the lengh ix X : Y

Then the ratio of the volume is X3 : Y3

Example 2: The ratio of a cylinder of volume 2970cm3  is 30mm. find the volume of a similar cylinder of radius 40mm.

Solution

Scale factor   =     40mm     =      4

30mm         3

Volume ratio  =  43

33

V            =    43

2970          33

Cross-multiply

V = 7040cm3

The volume of the cyclinder is 7040 cm3

READDING ASSIGNMENT

Essential Mathematics page 182

Exercise 19.2,  1-14

Exercise 19.1 ; 1- 19

WEEKEND ASSIGNMENT

Objectives

3         9            A. 27  B.  18   C.  6

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