Solve Problems Involving the Circumference and Area of Circles We are Learning to…… Solve Problems Involving the Circumference and Area of Circles

The circumference of a circle For any circle, π = circumference diameter or, π = C d We can rearrange this to make a formula to find the circumference of a circle given its diameter. Pupils should be asked to learn these formulae. C = πd

Finding the circumference given the radius The diameter of a circle is two times its radius, or d = 2r We can substitute this into the formula C = πd to give us a formula to find the circumference of a circle given its radius. C = 2πr

Finding the radius given the circumference Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? C 2π r = ? Link: A3 Formulae – changing the subject of a formula 12 2 × 3.14 = = 1.91 cm (to 2 d.p.)

Find the perimeter of this shape Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 13 cm 6 cm Perimeter = 3.14 × 13 + 6 + 6 = 52.82 cm

Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π × r × r radius or Area of a circle = πr2

Finding the area given the diameter The radius of a circle is half of its radius, or r = d 2 We can substitute this into the formula A = πr2 to give us a formula to find the area of a circle given its diameter. A = πd2 4

Find the area of this shape Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm. Area of circle = 3.14 × 6.52 13 cm 6 cm = 132.665 cm2 Compare this with slide 74, which finds the perimeter of the same shape. Area of rectangle = 6 × 13 = 78 cm2 Total area = 132.665 + 78 = 210.665 cm2

Area of a sector What is the area of this sector? Area of the sector = 72° 360° × π × 52 72° 5 cm 1 5 = × π × 52 = π × 5 Discuss how this area could be calculated before revealing the solution. The area of a sector is a fraction of the area of a full circle. We can find this fraction by dividing the angle at the centre by 360°. = 15.7 cm2 (to 1 d.p.) We can use this method to find the area of any sector.

Circumference and Area of a Circle The Circumference of a circle can be calculated using the formulae: C = 2πr or C = πd The Area of a circle can be worked out by using the formula: A = πr² Where d is the diameter, r is the radius and π = 3.14 to 2 decimal places Circles 3 Word Problems #s 2, 4, 6, 7, 9, 11, 12 & 14

Extra Practice Using the appropriate formula, work out the circumference and area for the following circles: 1. r = 4 cm Use π = 3.14 2. d = 7 cm The formulae are: 3. r = 6 cm C = 2πr 4. d = 9 cm C = πd 5. r = 7 cm A = πr²