Targeting Grade C SSM 3 Circles GCSE Mathematics

a.Know and use the vocabulary associated with circles b.Know and use the value of pi (π) c.Remember the formula for the circumference of a circle. d.Calculate the circumference of a circle given the length of the radius or the diameter e.Remember the formula for the area of a circle e.Calculate the area of a circle given either the length of the radius or the diameter f.Solve problems involving the circumference and area of a circle Questions Can you: Calculate the circumference of a circle Calculate the area of a circle Solve (word) problems involving the circumference and/or area of a circle. Try these questions If not you need to

Vocabulary and Definitions Circumference (Perimeter) – the distance all the way round the edge of the circle. Diameter – the distance from edge to edge passing through the centre of the circle Radius – the distance from the centre of the circle to the edge

π Find the value of π in the following three slides.

(To 2 decimal places) π =

(To 1 decimal places) π =

(To 1 significant figure) π =

Circumference of a Circle Circumference (C) Diameter (d) Radius (r) C = π x d (C= πd) C=2 x π x r (C=2 πr)

Circumference Calculate the circumference of the circles on the following slides

Example A circular dish has a diameter of 9cm. Calculate the circumference of the dish. (Take π = 3.14) 9cm C = π x d C = 3.14 x 9 C = 28.26cm

Example A circle has a radius of 6cm. Calculate the circumference. (Take π = 3) 6 cm Radius = 6cm Diameter = 12 cm (twice the radius) C = π x d C = 3 x 12 C = 36cm

5 cm Practice 1: Find the Circumference C = (Take π = 3)

8 cm C = (Take π = 3) Practice 2: Find the Circumference

12 cm C = (Take π = 3) Practice 3: Find the Circumference

2 cm C = (Take π = 3) Practice 4: Find the Circumference

6 cm C = (Take π = 3.1) Practice 5: Find the Circumference

15 cm C = (Take π = 3.1) Practice 6: Find the Circumference Answers to all circumference practice questions

Practice answers - Circumference 1.C = π x d (π = 3, d = 5) so C = 3 x 5, C = 15cm. 2.C = π x d (π = 3, d = 8) so C = 3 x 8, C = 24cm. 3.C = π x d (π = 3, d = 12) so C = 3 x 12, C = 36cm 4.C = π x d (π = 3, r = 2, d is 4) so C = 3 x 4, C = 12cm 5.C = π x d (π = 3.1, d = 6) so C = 3.1 x 6, C = 18.6 cm 6.C = π x d (π = 3.1, d = 15) so C = 3.1 x 15, C = 46.5cm

Area of a circle The formula for the area of a circle is Area = π x radius x radius A = π x r x r A = π r ²

Example 1 - Area Work out the area of a circle with radius 5cm. (Take π = 3) 5cm Area = π r² A = π x r x r A = 3 x 5 x 5 A = 75cm²

Example 2 - Area Work out the area of a circle with diameter 14cm. Answer to 3 significant figures (Take π = 3.14) 8cm diameter = 16cm so radius is 8cm Area = π r² A = π x r x r A = 3.14 x 8 x 8 A = cm² A = 201cm² (to 3 s.f.)

5 cm A = (Take π = 3) Practice 1: Find the Area

4 cm A = (Take π = 3) Practice 2: Find the Area

20 cm C = A = (Take π = 3.14) Practice 3: Find the Circumference and Area Answers to all area practice questions

Practice answers - Area 1.A = π r ² (π = 3, r = 5) A = 3 x 5 x 5 A = 75cm² 2.A = π r ² (π = 3, r = 4) A = 3 x 4 x 4 A = 48cm². 3.A = π r ² (π = 3.14, d = 20 so the radius is 10cm.) A = 3 x 10 x 10 A = 300cm²

Questions

(i)The radius of a circle is 3.5 feet. Calculate the circumference of this circle (ii)Calculate the area of this circle (4) Take π = 3.14 Answer The radius is 3.5 so the diameter is 7 feet (i)C = π x d C = 3.14 x 7 C = cm (ii)A = π r ² A = π x r x r A = 3.14 x 3.5 x 3.5 A = cm² A = 38.46cm² (2dp )

(a)Calculate the area of a circle with radius 1.2 cm (2) (b)What is the radius of a circle with an area of 66 cm²? (3) Take π = 3.14 Answer The radius is 1.2 cm (a) A = π r ² A = π x r x r A = 3.14 x 1.2 x 1.2 A = cm² A = 4.52cm² (2dp) (b)A = π r ² 66 = π x r ² 66 = 3.14 x r ² r =  (66 ÷3.14) r = 4.58cm (2dp)

a)A circle has a diameter of 7 cm. (i)Calculate the circumference of this circle ………………………………………. (ii)Calculate the area of this circle ……………………………………… (b)A plastic beaker has a height of 10 cm and a circular base of diameter 7 cm. Calculate the volume of the beaker Take π = 3.14 Answer The diameter is 7cm so the radius is 3.5cm (a) (i) C = 3.14 x 7 C = cm (ii)A = π r ² A = π x r x r A = 3.14 x 3.5 x 3.5 A = cm² A = 38.46cm² (2dp) (b)V = area of cross section x h V = x 10 V = cm³