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Mathematics

Grade 8

Rational numbers, circles and triangles

Module 13

The characteristics of a circle

Activity 1

Discovering the characteristics of a circle

[lo 3.1, 4.2.1, 3.4]

  1. Try to copy the following design, using a pair of compasses only:

2. Draw a circle of any size. Refer to a textbook or any other source of information to help you indicate the following on the circle:

2.1 Centre: T

2.2 Diameter (Name it PQ .)

2.3 Radius: TS

2.4 Any arc: FG

2.5 Sector: PTW (shade this portion.)

2.6 Chord: KL

2.7 Use a coloured pencil to indicate where you would determine the circumference of the circle.

3. Refer to your sketch to answer the following questions:

3.1 What is characteristic of TW , PT , TS and TQ ?

3.2 Measure P T ˆ W size 12{P { hat {T}}W} {} .

3.3 What is the size of P T ˆ Q size 12{P { hat {T}}Q} {} ?

3.4 What do we call this type of angle?

4. Construct the following with the help of a pair of compasses:

4.1 a circle with a diameter measuring 4 cm

4.2 a circle with a radius of 1,5 cm

5. How would you go about constructing a circle of 4 m?

  • Plan:

Activity 2

Discovering the circumference of a circle and dealing with related problems

[lo 4.2.2, 4.3.1, 4.3.2, 4.3.3, 4.4, 4.5.1]

1. Make use of about four bottles / cups of different sizes. Use a length of string and measure the diameter of each of the bottles to complete the following table:

circumference (O) diameter (m/d) O ÷ m/d
Bottle 1
Bottle 2
Bottle 3
Bottle 4
  • What is noticeable in the last column?

circumference ÷ diameter

1.2 What is the term used for the answer in the last column?

1.3 Name two values that can be used for π: ...................... or ......................

1.4 Which formula can therefore be used to calculate the circumference of any circle?

2. We could also deduce this formula from a circle by proceeding as follows:

2.1 Draw a circle with centre P and radius 25 mm on a sheet of paper.

2.2 Cut out the circle and place a mark anywhere on the edge of the cut circle.

2.3 Draw a line (use a ruler) across the remaining area of the sheet of paper. Roll the circle (cut out disk) on its edge along this line (place the mark on the edge of the circle at the beginning of the ruled line. Mark the spot where the rotation is completed on the line when the rolled circle has completed a full rotation.

2.4 Use your ruler to measure the marked distance.

  • Distance: ......................... mm

2.5 What term would we use to describe the distance that was measured in 2.4?

2.6 Use your calculator to calculate the following:

  • circumference ÷ diameter = ..................... ÷ ..................... = ........................

2.7 What term do we use to describe the answer that you have obtained?

3. What do we actually mean when we say that the wheel of a bicycle has completed a full rotation?

4. Write the formula for calculating the circumference of a circle on the following line and answer the questions that follow:

  • Circumference = ..................................................

4.1 How would you calculate the radius of a circle when the circumference is provided?

  • Radius ( R ) = ..................................................

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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