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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 price elasticity of demand and its degrees. also explain factors determing price elasticity of demand?
Yutansh Reply
Price elasticity of demand (PED) is use to measure the degree of responsiveness of Quantity demanded for a given change on price of the good itself, certis paribus. The formula for PED = percentage change in quantity demanded/ percentage change in price of good A
its is necessarily negative due to the inverse relationship between price and Quantity demanded. since PED carries a negative sign most of the time, we will usually the absolute value of PED by dropping the negative sign.
PED > 1 means that the demand of the good is price elasticity and for a given increase in price there will be a more then proportionate decrease in quantity demanded.
PED < 1 means that the demand of the good is price inelasticity and for a given increase in price there will be a less then proportionate decrease in quantity demanded.
The factors that affects PES are: Avaliablilty of close substitutes, proportion of income spent on the good, Degree of necessity, Addiction and Time.
Calculate price elasticity of demand and comment on the shape of the demand curve of a good ,when its price rises by 20 percentage, quantity demanded falls from 150 units to 120 units.
Helen Reply
5 %fall in price of good x leads to a 10 % rise in its quantity demanded. A 20 % rise in price of good y leads to do a 10 % fall in its quantity demanded. calculate price elasticity of demand of good x and good y. Out of the two goods which one is more elastic.
what is labor
Grace Reply
labor is any physical or mental effort that helps in the production of goods and services
what is profit maximizing level of out put for above hypothetical firm TC = Q3 - 21Q2 + 600 + 1800 P = 600 MC = 3Q2 - 42Q + 600
Sosna Reply
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
sorry it the mistake answer it is question
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
The formula for calculation income elasticity of demand is the percent change in quantity demanded divided by the percent change in income.
what is labor productivity
Lizzy Reply
if the demand function is q=25-4p+p² 1.find elasticity of demand at the point p=5?
Puja Reply
what are some of the difference between monopoly and perfect competition market
Obeng Reply
n a perfectly competitive market, price equals marginal cost and firms earn an economic profit of zero. In a monopoly, the price is set above marginal cost and the firm earns a positive economic profit. Perfect competition produces an equilibrium in which the price and quantity of a good is economic
what are some characteristics of monopoly market
Obeng Reply
explicit cost is seen as a total experiences in the business or the salary (wages) that a firm pay to employee.
Idagu Reply
what is price elasticity
it is the degree of responsiveness to a percentage change in the price of the commodity
economics is known to be the field
John Reply
what is monopoly
Peter Reply
what is taxation
is the compulsory transfer of wealth from the private sector to the public sector
why do monopoly make excess profit in both long run and short run
Adeola Reply
because monopoly have no competitor on the market and they are price makers,therefore,they can easily increase the princes and produce small quantity of goods but still consumers will still buy....
how to identify a perfect market graph
Adeola Reply
what is the investment
investment is a money u used to the business
investment is the purchase of good that are not consumed today but are used in the future to create wealth.
investment is the good that are not consumed
What is supply
 Supply represents how much the market can offer.
it is the quantity of commodity producers produces at the market
what is the effect of scarce resources on producers
Phindu Reply
explain how government taxes and government producer subsidies affect supply
what is economic
Charles Reply
what are the type of economic
macroeconomics,microeconomics,positive economics and negative economics
what are the factors of production
process of production
Basically factors of production are four (4) namely: 1. Entrepreneur 2. Capital 3. Labour and; 4. Land but there has been a new argument to include an addition one to the the numbers to 5 which is "Technology"
what is land as a factor of production
what is Economic
economics is how individuals bussiness and governments make the best decisions to get what they want and how these choices interact in the market
Economics as a social science, which studies human behaviour as a relationship between ends and scarce means, which have alternative uses.
Economics is a science which study human behaviour as a relationship between ends and scarce means
Economics is a social sciences which studies human behavior as a relationship between ends and scarce mean, which have alternative uses.....
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris 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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