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Circles

Circles. Finding the Circumference. You can find the circumference of a circle by using the formula- Circumference = π x diameter. For Example- Area= π x 10 = 31.41592654.... = 31.4 cm (to 1 dp). 10cm.

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Circles

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  1. Circles

  2. Finding the Circumference You can find the circumference of a circle by using the formula- Circumference = π x diameter For Example- Area= π x 10 = 31.41592654.... = 31.4 cm (to 1 dp) 10cm

  3. You can find the circumference of a circle by using the formula- Circumference = π x diameter For Example- Area= π x 10 = 31.41592654.... = 31.4 cm (to 1 dp) ANSWERS 10cm • Find the Circumference of a circles with: • A diameter of : • 8cm • 4cm • 11cm • 21cm • 15cm • A radius of : • 6cm • 32cm • 18cm • 24cm • 50cm HOME

  4. Finding the Area You can find the area of a circle by using the formula- Area= π x Radius2 For Example- Area= π x 72 = π x 49 = 153.93804 = 153.9 (to 1dp) cm2 7cm

  5. Compound Area and Perimeter Here we will look at shapes made up of triangles, rectangles, semi and quarter circles. Find the area of the shape below: 10cm Area of this semi circle = π r2 ÷ 2 = π x 52 ÷ 2 = π x 25÷ 2 =39.3 cm2 (1dp) 8cm 10cm Area of this rectangle= 8 x10 =80cm2 Area of whole shape = 80 + 39.3 = 119.3 cm2

  6. Compound Area and Perimeter Find the perimeter of the shape below: 10cm Circumference of this semi circle = πd ÷ 2 = π x 10÷ 2 =15.7 cm (1dp) 8cm 10cm Perimeter of this rectangle= 8 + 8 + 10 =26cm (don’t include the red side) Perimeter of whole shape = 26 + 15.7 = 31.7 cm

  7. Compound Area and Perimeter Find the areaof the shape below: 5cm Area of this quarter circle = π r2 ÷ 4 = π x 52 ÷ 4 = π x 25÷ 4 =19.7 cm2 (1dp) 10cm 11cm Area of whole shape = 110+ 19.7 = 129.7cm2 Area of this rectangle 10 x 11=110

  8. Compound Area and Perimeter Work out all missing sides first Find the perimeter of the shape below: ? 5cm Circumference of this quarter circle = πd ÷ 4 = π x 10÷ 4 (if radius is 5, diameter is 10) =7.9 cm (1dp) 6cm 5cm 10cm 10cm 11cm Area of whole shape = 42+ 7.9 = 49.9cm Add all the straight sides= 10+10 + 11+ 5 + 6= 42cm

  9. Questions Find the perimeter and area of these shapes, to 1 decimal place 2cm 3 1 2 12cm 10cm 20cm 6cm 11cm 4cm 17cm 4cm 6cm Do not worry about perimeter here Do not worry about perimeter here 6 4 5 10cm 10cm 5cm 5cm 5cm 20cm 12cm HOME

  10. Volume of Cylinders Here we will find the volume of cylinders Cylinders are prisms with a circular cross sections, there are two steps to find the volume 1) Find the area of the circle 1) Multiple the area of the circle by the height or length of the cylinder

  11. Volume of Cylinders 2 EXAMPLE- find the volume of this cylinder 4cm • Find the area of the circle • π x r2 • π x 42 • π x 16 = 50.3 cm2 (1dp) 10cm 2) Multiple the area of the circle by the height or length of the cylinder 50.3 (use unrounded answer from calculator) x 10 = 503cm3

  12. Questions Find the volume of these cylinders, to 1 decimal place 3 ANSWERS 1 2 4cm 3cm 5cm 12cm 10cm 15cm 6 3cm 4 5 2cm 7cm 18cm 11.3cm 14cm HOME

  13. Volume of Cylinders 2 EXAMPLE- find the height of this cylinder 4cm • Find the area of the circle • π x r2 • π x 42 • π x 16 = 50.3 cm2 (1dp) h 2) Multiple the area of the circle by the height or length of the cylinder 50.3 x h = 140cm3 Rearrange this to give h= 140 ÷ 50.3 h=2.8 cm Volume= 140cm3

  14. Volume of Cylinders EXAMPLE- find the radius of this cylinder r • Find the area of the circle • π x r2 2) Multiple the area of the circle by the height or length of the cylinder π x r2 x 30 = 250cm3 94.2... x r2 = 250 Rearrange this to give r2 = 250 ÷ 94.2 r2 =2.7 (1dp) r= 1.6 (1dp) cm 30cm Volume= 250cm3

  15. Questions Find the volume of these cylinders, to 1 decimal place 3 1 2 4cm 3cm 5cm h h h volume= 320cm3 volume= 120cm3 volume= 100cm3 5 6 r r r 4 12cm 8cm 14cm volume= 90cm3 volume= 150cm3 volume= 200cm3 HOME

  16. Volume of Spheres The formula for the volume of a sphere is e.g A= 4/3 x π x 103 A= 4/3 x π x 1000 A=4188.8 cm3 (1 dp) 10cm

  17. Volume of Cones The formula for the volume of a cone is 10cm e.g A= 1/3 x π x 42 x 10 A= 1/3 x π x 16 x 10 A=167.6 cm3 (1 dp) 4cm

  18. ANSWERS Questions Find the volume of these spheres, to 1 decimal place 3 1 2 10cm 20cm 5cm 15cm 12cm 13cm 6 4 5 3cm 9cm 4cm HOME

  19. Circle Formulae HOME

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