Properties of a Circle Diagram Source:
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1 Properties of a Circle Diagram Source: Definitions: Circumference (c): The perimeter of a circle is called its circumference Diameter (d): Any straight line drawn through the centre and terminating at both ways by the circumference is called a diameter. Origin: Origin refers to the center of a circle Pi: An approximate value of is /7 which is correct to two decimal places. A more accurate value of is which is correct to five decimal places. Pi = C/d Radius (r) - radii: The constant distance of every point on the circle from its centre is called the radius of the circle. It is half of the diameter.
2 Enrichment Terms: These terms will not be tested Arc: A continuous piece of a circle is called an arc. In other words, any portion of the circumference of a circle is called an arc. Chord: A straight line joining any two points on the circumference of a circle is called a chord. Sector: A sector is that part of a circle, which lies between an arc and two radii joining the extremities of the centre. The most important sector is a quadrant, which is one-fourth of the circle. Tangent of a circle: It is a line perpendicular to the radius that touches only one point on the circle. Formulas for Circles Circumference (C) of a circle: C = Pi (r) or Pi (d) r = 3.5 cm r = 3.5 cm Find the measurement of the circumference. Solve for C. C = 3.14 ( x 3.5 cm) C = 3.14 x 7 cm 3.14 x The circumference of the circle is 1.98 cm.
3 Area (A) of a circle: A = Pi (r ) r = 5.9 mm r = 5.9 mm Find the area for the circle. Solve for A. A = 3.14 (5.9 x 5.9) x A = 3.14 x decimals x 3.14 decimals decimal places mm Areas of dimensional geometric shapes are squared. The area of the circle is mm.
4 Area of a Parallelogram A parallelogram is a polygon. It is a four sided plane figure with opposite sides parallel and the same length. Ex. Area of a parallelogram equals base multiplied by the height A = b x h or A = bh If a parallelogram has a base of 9 cm and the height is 6 cm, what is the area of the figure? A = bh A = b x h A = 9 cm x 6 cm A= 54 cm The area of the parallelogram is 54 cm.
5 If you are provided with the area of a parallelogram and one other measurement of either base of height, it is possible to find the missing measurement. Finding height of a parallelogram: Divide the area by the base to find the height measurement of a parallelogram. h = A / b h = 54 cm / 9 cm h = 6 cm The height of the parallelogram is 6 cm. Finding base of a parallelogram: Area = 54 cm and the base is 9 cm. Divide the area by the height to find the base measurement of a parallelogram. b = A / h b = 54 cm / 6 cm b = 9 cm The base of the parallelogram is 9 cm.
6 Area of a Triangle A triangle is a polygon. It is a three sided figure. Ex. Area of a triangle equals half of base multiplied by height. A = 1 / (b x h) A = bh / If a triangle has a base of 8 cm and a height of 5 cm, what is the area of the figure? A = bh / A = (8 cm x 5 cm) / A = 40 cm / A = 0 cm The area of the triangle is 0 cm.
7 If you are provided with the area of a triangle and one other measurement of either base of height, it is possible to find the missing measurement. Finding height of a triangle: Divide twice the area by the base to find the height measurement of a parallelogram. h = A / b h = ( x 0 cm ) / 8 cm h = 40 cm / 8 cm h = 5 cm The height of the triangle is 5 cm. Finding base of a triangle: Divide twice the area by the height to find the base measurement of a parallelogram. b = A / h b = x 0 cm / 5 cm b = 40 cm / 5 cm b = 8 cm The base of the triangle is 8 cm.
8 More to do with Area: Example #1: h = 6 cm b = 6 cm Area of the parallelogram = bh A = 6 cm x 6 cm A = 36 cm Area of the circle = Pi r A = 3.14 x 3 cm x 3 cm A = 3.14 x 9 cm A = 8.6 cm Area of the shaded region = Area of the parallelogram subtract Area of the circle A = 36 cm cm
9 Example #: h = 7 cm b = 5 cm Area of the parallelogram = bh A = 5 cm x 7 cm A = 35 cm Area of the triangle= bh / A = (5 cm x 7 cm) / A = 35 cm / A = 17.5 cm A of the region outside of the triangle, but within the parallelogram = A of the parallelogram - A of the triangle A = 35 cm cm A = 6.74 cm
10 Circle Graphs 0 A circle has 360 round its origin Finding angle measurements of a circle graph: 30% 35% 30% + 35% + 5% + 10% = 100 Convert the sector percent to a decimal. 10% = % = = = x 100 = 100 Multiply 360 by the sectors decimal to find the sector s angle measurement. 360 x 0.30 = x 0.35 = x 0.5 = x 0.10 =
11 Finding Percent of a circle: 1 = 100% of the circle (10%) 1 (57%) 7 (33%) Divide the sector s # by 1, then multiply by 100 to find the percentage of the sector. 1 1 = x 100 = 57% 1 = * x 100 = 10% 7 1 = x 100 = 33% x 100 = 100%
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