AREA AND CIRCUMFERENCE OF A CIRCLE circumference di

AREA AND CIRCUMFERENCE OF A CIRCLE

circumference di The diameter (d) of a circle is twice the radius (r). am et er The perimeter of a circle is called the circumference (C). rad ius

Consider dividing a circle into 8 equal sectors: rearranging the sectors of the circle gives

Now consider dividing the circle into 12 equal sectors: rearranging the sectors of the circle gives r half circumference The more sectors there are, the closer the area gets to being a rectangle.

Examples 1 Calculate a the circumference b the area of the circle. a 8 cm b

Examples 2 Calculate a the circumference b the area of the circle. a 3. 7 cm b

Examples 3 The radius of the circle is 5 cm. The circle touches all four sides of the square. Calculate the shaded area. 10 cm

Examples 4 The radius of the large circle is 8 cm. The radius of the small circle is 5 cm. Calculate the shaded area.

Examples 5 The radius of the circle is 3 cm. The vertices of the square lie on the circumference of the circle. Calculate the shaded area. 6 cm Using Pythagoras x x

Examples 6 The area of the circle is 200 cm 2. Find the value of r. r cm

Semicircles and quadrants A semicircle is half a circle. A quadrant is quarter of a circle.

Examples 1 Calculate a the perimeter b the area of the semicircle. a 10 cm b

Examples 2 Calculate a the perimeter b the area of the quadrant. a 9 cm b

Examples 3 The perimeter of the quadrant is 50 cm. Calculate the value of r. r cm

Examples 4 The diagram shows four identical circles of radius 4 cm. Calculate the shaded area.

Arcs and sectors An arc is part of the circumference of a circle. arc sector A sector of a circle is a region bounded by an arc and two radii.

Examples 1 Find a the area of sector OAB b the length of arc AB c the perimeter of sector OAB. a b c A B O

Examples 2 Find a the area b the perimeter of the shape. a 126° 7 m b 3 m