GCSE Mathematics Targeting Grade C SSM 3 Circles
Know and use the vocabulary associated with circles • Know and use the value of pi (π) • Remember the formula for the circumference of a circle. • Calculate the circumference of a circle given the length of the radius or the diameter • Remember the formula for • the area of a circle • Calculate the area of a circle given either the length of the radius or the diameter • 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 πin 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) C = π x d C = 3.14 x 9 C = 28.26cm 9cm
6 cm Example A circle has a radius of 6cm. Calculate the circumference. (Take π = 3) Radius = 6cm Diameter = 12 cm (twice the radius) C = π x d C = 3 x 12 C = 36cm
Practice 1: Find the Circumference 5 cm C = (Take π = 3)
Practice 2: Find the Circumference 8 cm C = (Take π = 3)
Practice 3: Find the Circumference 12 cm C = (Take π = 3)
2 cm Practice 4: Find the Circumference C = (Take π = 3)
Practice 5: Find the Circumference 6 cm C = (Take π = 3.1)
Practice 6: Find the Circumference 15 cm C = (Take π = 3.1) Answers to all circumference practice questions
Practice answers - Circumference • C = π x d (π = 3, d = 5) so C = 3 x 5 , C = 15cm. • C = π x d (π = 3, d = 8) so C = 3 x 8, C = 24cm. • C = π x d (π = 3, d = 12) so C = 3 x 12, C = 36cm • C = π x d (π = 3, r = 2, d is 4) so C = 3 x 4, C = 12cm • C = π x d (π = 3.1, d = 6) so C = 3.1 x 6, C = 18.6 cm • 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) Area = π r² A = π x r x r A = 3 x 5 x 5 A = 75cm² 5cm
Example 2 - Area Work out the area of a circle with diameter 14cm. Answer to 3 significant figures (Take π = 3.14) diameter = 16cm so radius is 8cm Area = π r² A = π x r x r A = 3.14 x 8 x 8 A = 200.96 cm² A = 201cm² (to 3 s.f.) 8cm
Practice 1: Find the Area 5 cm A = (Take π = 3)
Practice 2: Find the Area 4 cm A = (Take π = 3)
Practice 3: Find the Circumference and Area 20 cm C = A = (Take π = 3.14) Answers to all area practice questions
Practice answers - Area • A = π r ² (π = 3, r = 5) A = 3 x 5 x 5 A = 75cm² • A = π r ² (π = 3, r = 4) A = 3 x 4 x 4 A = 48cm². • 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 • C = π x d • C = 3.14 x 7 • C = 21.98 cm • A = π r ² • A = π x r x r • A = 3.14 x 3.5 x 3.5 • A = 38.465cm² • A = 38.46cm² (2dp)
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 = 4.5216cm² • A = 4.52cm² (2dp) • 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 = 21.98 cm • A = π r ² • A = π x r x r • A = 3.14 x 3.5 x 3.5 • A = 38.465cm² • A = 38.46cm² (2dp) • V = area of cross section x h • V = 38.465 x 10 • V = 384.65 cm³
