Investigate the area of a disc compared to a square. (i) Working with a classmate, draw a square of side 10 cm. Then, using a compass, draw a circle which fi ts exactly inside this square (as shown).
(ii) What percentage of the area of the square is covered by the circle?
(iii) Repeat this activity with other circles drawn inside squares but change the size of the square used in each case.
What have you discovered about the percentage area taken up by a circle which fi ts exactly inside a square?
Practice questions 16·2 1.
10 cm
10 cm
(a) Find the value of π for circles with the following measurements: (i) Diameter = 20 cm, circumference = 62·80 cm (ii) Radius = 4 cm, circumference = 25·12 cm (iii) Diameter = 180 cm, circumference = 5 652 mm
(b) What do you notice about your answers to part (a)?
2. Write down the type of circle represented by each diagram below, i.e. circles, semicircles, discs or half discs.
(i) (ii) (iii) (iv)
3. (a) Draw the following circles using a compass and a ruler. (i)
(ii) 6 cm 5 cm 4.5 cm
(b) Taking π = 3·14 , fi nd the circumference of each of the circles in part (a), correct to two decimal places.
(c) Taking π = 22
__ 7 , fi nd the circumference of each of the circles in part (a), correct to two decimal places.
(d) Find, in terms of π , the circumference of each of the circles in part (a). 57 mm (iii)