Lesson Notes By Weeks and Term - Junior Secondary School 3

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 ∆ABC, 

In ∆XYZ, 0       

Since then corresponding angles are equal, ∆ABC and ∆XYZ are similar 

Scale factor  =     4     =       1

              12    3

Area factor  = (1/3)2    = 1/9

Area of ∆XYZ     =     1

Area of ∆ABC          9

Area of ∆XYZ     =     1

          48          9

Area of ∆XYZ     =     48

                                    9            =  5.333cm2 

Area of ∆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

1. An object has an area of 3.2cm2 on a map is 1: 1000, find the actual area of the object in m2   .
2. Two similar circles have corresponding radio in the ratio 4:9. What is the ratio of their area.

Objectives

1. If the scale factor is 2:3, what is the area factor   A.  4: 6   b. 6: 4  C. 4:9
2. If the area factor is 4:9, what is the volume factor  A.  8: 27   B.  64:81   C.  27:8
3. Area factor is the _____ of scale factor  A. cube  B. square  C. root
4. The corresponding altitudies of two similar triangles are 8cm and 5cm. Find the ration of their areas?  A. 25:16  B.  64:25  C. 64:10
5. If    2    =   x       find x

      3         9            A. 27  B.  18   C.  6