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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

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studies of microbes
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Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
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they make spores
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food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
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Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
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This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
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Examples of thermophilic organisms
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Give Examples of thermophilic organisms
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Prevent foreign microbes to the host
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they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
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cell is the smallest unit of life
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Innocent
cell is the structural and functional unit of life
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is the fundamental units of Life
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There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
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Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
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part of a tissue or an organ being wounded or bruised.
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Binomial nomenclature
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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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