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4.2 How would you calculate the diameter of a circle when the circumference is provided?

  • Diameter ( d ) = ..................................................

Now you should be able to answer any question dealing with the diameter, radius or circumference of a circle or wheel or any circular object.

5. Use your pocket calculator to calculate the circumference of each of the following circles:

Note this : Always write out the formula before you start.(π = 3,14).

5.1 r = 230 mm

5.2 r = 1,45 cm (answer to 2 decimal figures)

6. Determine the circumference of each of the following without the use of a pocket calculator.

Note this : Always write out the formula before you start.(π = 22 7 size 12{ { {"22"} over {7} } } {} )

6.1 r = 14 cm

6.2 d = 35 cm

  1. Calculate the radius of the following circle:

You may use your pocket calculator, but you have to show all the steps of the calculation. (π= 22 7 size 12{ { {"22"} over {7} } } {} )

7.1 circumference 242 mm

8. How many rotations will the wheel of a mountain bike complete over a distance of 7,5 m if the diameter of the wheel is 67 cm?

Activity 3

Discovering the area of a circle and solving related problems

[lo 4.2.1, 4.5.1, 4.3]

1. Can you remember the formula for calculating the area of a rectangle?

2. Draw a circle with centre O and a radius of 60 mm on a sheet of paper. Divide the circle into 32 equal sectors. Use red for colouring 16 sectors and blue for the remaining 16 sectors.

3. Cut out all 32 sectors and arrange them in line in such a way that the segments eventually form a rectangular paving design.

Paste your triangles in the following space

4. Measure both the length and breadth of the rectangle. Use the formula from no. 1 to calculate the area of the rectangle.

5. What do you deduce with regard to the rectangle and the circle that you have drawn in no. 2?

6. Which unit of measurement is used for calculating area?

7. Provide the formula for calculating the area of any circle.

8. Calculate the area of the circle you have drawn in no. 2 with the help of the formula from no. 7.

What do you notice?

9. Calculate the area of each of the following circles without making use of a pocket calculator.

  • (π = 22 7 size 12{ { {"22"} over {7} } } {} )

9.1 r = 14,7 cm 9.2 d = 56,49 cm

10. Calculate the area of the shaded parts.

  • You may use your pocket calculator for this. (π = 3,14)

Assessment

LO4
MeasurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.
We know this when the learner:
4.2 solves problems involving:
4.2.1 length;
4.2.2 perimeter and area of polygonals and circles;
4.3 solves problems using a range of strategies including:
4.3.1 estimating;
4.3.2 calculating to at least two decimal positions;
4.3.3 using and converting between appropriate SI units;
4.4 describes the meaning of and uses π size 12{π} {} in calculations involving circles and discusses its historical development in measurement;
4.5 calculates, by selecting and using appropriate formulae:
4.5.1 perimeter of polygons and circles;
4.5.2 area of triangles, rectangles circles and polygons by decomposition into triangles and rectangles;
  • investigates (alone and / or as a member of a group or team) the relationship between the sides of a right-angled triangle to develop the Theorem of Pythagoras;
4.9 uses the Theorem of Pythagoras to calculate a missing length in a right-angled triangle leaving irrational answers in surd form (√);
4.10 describes and illustrates ways of measuring in different cultures throughout history (e.g. determining right angles using knotted string leading to the Theorem of Pythagoras).

Memorandum

ACTIVITY 2

5.1 O = π size 12{π} {} x d

O = π size 12{π} {} x 460

O = 1 444,4 mm

5.2 C = π size 12{π} {} x d

C = π size 12{π} {} x 2,9

C size 12{ approx } {} 9,11 cm

6.1 C = π size 12{π} {} x d

C = 22 7 1 size 12{ { {"22"} over { { {7}} rSub { size 8{1} } } } } {} x 2 8 4 1 size 12{ { { { {2}} { {8}} rSup { size 8{4} } } over {1} } } {}

C = 88 cm

6.2 C = π size 12{π} {} x d

C = 22 7 1 size 12{ { {"22"} over { { {7}} rSub { size 8{1} } } } } {} x 3 5 5 1 size 12{ { { { {3}} { {5}} rSup { size 8{5} } } over {1} } } {}

C = 110 cm

7.1 C = π size 12{π} {} x d

242 = 22 7 size 12{ { {"22"} over {7} } } {} x d

242 1 size 12{ { {"242"} over {1} } } {} x 22 7 size 12{ { {"22"} over {7} } } {} = d

size 12{∴} {} d = 77 mm

8. C = π size 12{π} {} x d 750 ÷ 210,38 cm

= 3,14 x 67 cm = 3,6 revolutions

= 210,38 cm

ACTIVITY 3

9. A = π size 12{π} {} x r 2

= 22 7 size 12{ { {"22"} over {7} } } {} x 14 , 7 1 size 12{ { {"14",7} over {1} } } {} x 14 , 7 1 size 12{ { {"14",7} over {1} } } {}

= 679,14 cm 2

  • r = 28,25

A = 2 505,92 cm 2

10. A B

(3,14 x 15 2 ) – (3,14 x 15 2 ) (14,5) 2 – (3,14 x 7,25 2 x 1 2 size 12{ { {1} over {2} } } {} )

= 706,5 – 78,5 = 210,25 – 82,52

= 628 cm 2 = 127,73 cm 2

11. (40 x 40) – (3,14 x 15 2 )

= 1 600 – 706,5

= 893,5 cm 2

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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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