Volume Calculate the volume of spheres pyramids cones

Key vocabulary Formula Substitute Area of a cross-section

Volume Which of the solids holds the most stuff? (Put another way, which has

Volume of a sphere Learn the formula: - r=3 cm

Volume of a square based pyramid Learn the formula: 1/3 x base x height

Volume of a cone Same as a pyramid: 8. 1 cm 9 cm Area

Practice (1) solutions For these questions, use r=3 cm and h=5 cm Find the

Practice (2) solutions = 1/3 x base x height

Practice (2) solutions = 1/3 x base x height = 1/3 x π x

Practice (2) solutions = 4/3 x π x 83 = 2144. 660585. . .

Practice (2) solutions Area of cone = 1/3 x base x height 22 –

Problem solving and reasoning 8 cm 22 cm Volume Oil is used to fill

Problem solving and reasoning A cone and a hemisphere have the same volume and

Practice (3) solutions Volume of water originally = 12 x 11 x 8 =

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Volume Calculate the volume of spheres, pyramids, cones and composite solids. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key vocabulary Formula Substitute Area of a cross-section

Volume Which of the solids holds the most stuff? (Put another way, which has the biggest volume? ) 6 cm 42. 4 cm 3 3 cm 6 cm 54 cm 3 3 cm 4 cm 3 cm Click on a solid to reveal its volume. 64 cm 3 4 cm

Volume of a sphere Learn the formula: - r=3 cm

Volume of a square based pyramid Learn the formula: 1/3 x base x height Height = 5. 2 cm Find the area of the base: 6 cm Substitute that in to the formula: This works for all types of pyramid – be it a tetrahedron or a cone or a pyramid with an irregular base

Volume of a cone Same as a pyramid: 8. 1 cm 9 cm Area of base: 8 cm Substitute into formula:

Practice (1) solutions For these questions, use r=3 cm and h=5 cm Find the volume of: 1) A square based pyramid, base length of 2 cm. 2) A cone 3) A sphere

Practice (2) solutions = 1/3 x base x height

Practice (2) solutions = 1/3 x base x height = 1/3 x π x 5. 72 x height For height, use Pythagoras’ theorem: Height = √(12. 62 -5. 72) = 11. 23699. . . Volume = 1/3 x π x 5. 72 x 11. 23699. . = 382. 3 cm 3

Practice (2) solutions = 1/3 x base x height

Practice (2) solutions = 4/3 x π x 83 = 2144. 660585. . . Hemisphere so must divide by 2 =1072. 3 cm 3

Practice (2) solutions Area of cone = 1/3 x base x height 22 – radius (7) = 15 Area of hemisphere

Problem solving and reasoning d= 8 cm

Problem solving and reasoning 8 cm 22 cm Volume Oil is used to fill the cone to burn as a light. Oil comes in 1 litre bottles and is £ 5. 50 per bottle. Jake has £ 10, is that enough to fill the cone? Remember to convert from cm 3 to litres AND to make a decision. = 1/3 xπx 82 x 22 =1474. 5 cm 3 = 1. 47 litres (as 1000 cm 3 = 1 litre) So, 2 litres are needed 2 x 5. 5 = £ 11 – not enough money

Problem solving and reasoning A cone and a hemisphere have the same volume and the same radius. What is the height of the cone in terms of r? volume of hemisphere volume of cone

Practice (3) solutions Volume of water originally = 12 x 11 x 8 = 1056 cm 3 New volume of water = 1560 + 180 cm 3 = 1236 cm 3 = 12 x 11 x new height New height = 9. 36 cm Rise = 9. 36 – 8 = 1. 36 cm

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