- circle is a round, two dimensional shape that looks similar to the letter ‘O’.
- In strict mathematical language, circle refers to the boundary of the shape while ‘disk’ is used to refer to the whole shape, including the inside.
- A straight line from the center of a circle to the edge is called the radius.
- A straight line that passes from one side of a circle to the other through the center is called the diameter.
- The distance around the outside of a circle is called the circumference.
- All points on the edge of a circle are the same distance to the center.
- The value of Pi (π ) to 2 decimal places is 3.14, it comes in handy when working out the circumference and area of a circle.
- The circumference of a circle can be found with the following formula: Circumference = π d
- The area of a circle can be found with the following formula: Area = π r²
- An arc is part of the circumference of a circle.
- A chord is a straight line joining two points on a circle, the diameter is an example of a chord (the longest possible one).
- A segment is the region between a chord and the arc it joins.
- A tangent is a straight line that touches a single point of a circle.
- A sector is the region between an arc and two radii.
- The full arc of a circle measures 360 degrees.
- A semicircle is a shape that forms half a circle, the arc of a semicircle measures 180 degrees.
- Circles have a high level of symmetry.
- A circle has the shortest perimeter of all shapes with the same area.
- The circle shape is a favorite of humans and can be seen in many designs.
- The invention of the wheel (a circle shape) was one of the most important in human history.
Area of a Circle Equipment: You will need a compass, pair of scissors, ruler and protractor for this activity.To discover a formula for the area of a circle.Purpose: Step 1: Using the compass, draw a circle of radius 7 cm. Then mark the circle's centre and draw its radius.Step 2: Place the centre of the protractor at the centre of the circle and the zero line along the radius. Then mark every 30º around the circle.Step 3: Using a ruler and a pencil, draw lines joining each 30º mark to the centre of the circle to form 6 diameters. The diagram thus obtained will have 12 parts as shown below.Step 4: Colour the parts as shown below.Step 5: Cut out the circle and then cut along the diameters so that all parts (i.e. sectors) are separated.Step 6: Arrange all of the sectors to make a shape that approximates a parallelogram as shown below.Step 7: Using a ruler, measure the base and the height of the approximate parallelogram obtained in Step 6.Questions:1. Calculate the area of the figure in Step 6 by using the formula: 2. What is the area of the circle drawn in Step 1? 3. It appears that there is a formula for calculating the area of a circle. Can you discover it? Formula for the Area of a Circle From the above activity, it is clear that by arranging the sectors of the circle as a parallelogram that: Remember:The area, A, of a circle is given by the following formula where r is the radius of the circle:Example 8 Solution:So, the area is 616 m2. Note:To find the area of a region enclosed within a plane figure, draw a diagram and write an appropriate formula. Then substitute the given values and use a calculator, if necessary, to obtain the required area. Example 9Find the area of a circle of whose diameter is 11 cm using π = 3.14. Round your answer to 2 decimal places.Solution: So, the area is 94.99 cm2. Numbers, numbers everywhere , There seems to be so many different types That I can’t get them all clear! Today we are detectives on case to find out more about numbers. You will be given the worksheet that is in the file below to complete based on types of numbers.
Use the links below to assist you with your mission. LINKS Triangles A triangle has three sides and three angles The three angles always add to 180°Equilateral, Isosceles and Scalene There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles:Equilateral Triangle Three equal sides Three equal angles, always 60°Isosceles Triangle Two equal sides Two equal anglesScalene Triangle No equal sides No equal anglesWhat Type of Angle? Triangles can also have names that tell you what type of angle is inside:Acute TriangleAll angles are less than 90° Right TriangleHas a right angle (90°) Obtuse TriangleHas an angle more than 90° |
## ThoughtBe the best version of yourself possible. ## Archives
January 2014
## Categories |