Geometry II

 

Welcome to Class !!

We are eager to have you join us !!

In today’s Mathematics class, We will continue our lesson on Geometry. We hope you enjoy the class!

 

geometry ii maths classnotesng

 

 

GEOMETRY CONT’D

Areas and Volumes of similar shaped

Scale Factor (Length Ratio)

P          9cm              Q

A                  B

 

2                                         6cm

 

D    3          C

S                                    R

 

Scale factor = 93 or 62 = 31

Area factor   = (Scale factor)2

312 = 91  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,  <A   = 180 – (65 + 60)  = 55

In ∆XYZ, <Y  = 180 – (55-60) = 650

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

Scale factor = 412 = 13Area factor = 132 = 19Area of XYZArea of ABC = 19Area of XYZ48 = 19Area of XYZ × 9 = 48Area of XYZ = 489                              = 5.3333 cm2Area of XYZ = 5.3 cm2 to 2 s.f  

 

 

The volume of Similar Shapes

Volume factor = (Scale factor)3

If the ratio of the length is 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 = 40mm30mm = 43Volume ratio = 433 = 4333V2970 = 4333 Cross multiplyV × 27 = 2970 × 64V = 2970 × 6427 = 7040The volume of the cylinder is 7040 cm3

 

 

 

 

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about the Area of Plane Figures. We are very much eager to meet you there.

 

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