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Targeting Grade C

GCSE Mathematics. Targeting Grade C. SSM 5 Volume . If not you need. Can you… Calculate the volume of a cuboid? Can you calculate the volume of prisms (triangular, cylinder, trapezoidal)? Solve problems involving volumes of 3D shapes?

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Targeting Grade C

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  1. GCSE Mathematics Targeting Grade C SSM 5 Volume

  2. If not you need • Can you… • Calculate the volume of a cuboid? • Can you calculate the volume of prisms (triangular, cylinder, trapezoidal)? • Solve problems involving volumes of 3D shapes? • Can you work out a length if you have been given the volume? • Try some questions Practice 1: Remember the formula for volume of a cuboid. You will be given the formulae for the area of a trapezium and the volume of a prism, but you will need to know the formulae for the area of a circle and a triangle. Practice 2: Decide which formulae to use when calculating the volume. Practice 3: Substitute the values given into the correct formula. Questions:

  3. Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h

  4. Work out the volume of this cuboid V = l x b x h V = 15 x 6 x 10 V = 900cm³ A cuboid has Height = 3m Length = 9m Breadth =5m What is its volume? V = l x b x h V = 3 x 9 x 5 V = 135 m³ 10 cm 6 cm 15 cm Note that there are 3 dimensions so the units are cubic m or cm. Example

  5. Maxine has two boxes in the shape of cuboids. Box A measures 12·3cm by 6cm by 3cm Box B measures 9cm by 8·7cm by 2·8cm Maxine wants to use the box with the greater volume Give the letter of the box Maxine should use You must show all your calculations Practice 1 Answer

  6. Practice 1 answer Box A V = l x b x h V = 12.3 x 6 x 3 V = 221.4 cm³ Box B V = l x b x h V = 9 x 8.7 x 2.8 V = 219.24cm³ Box A has the greatest value

  7. Area of Circle The formula for the area of a circle Area = pi x radius x radius A = π x r x r A = πr²

  8. Area of a triangle The formula for the area of a triangle is Area = ½ x base x perpendicular height A = ½ x b x h. A = ½bh

  9. Calculate the volume of this trapezoidal prism Volume of prism is Area of cross section x length 19.62 x 10 196.2cm³ 10cm Example 10cm Area of cross section (trapezium) is ½ (a+b)h ½ (4.2 + 6.7) x 3.6 ½ x 10.9 x 3.6 ½ x 39.24 19.62cm² Remember 2 dimensions - units² 3 dimensions – units³

  10. Example Area of cross section (triangle) is ½ b x h ½ x 3 x 4 ½ x 12 = 6cm² Volume of prism is Area of cross section x length 6 x 11 = 66cm³

  11. (a) The cylinder has a radius of 4cm and a height of 15cm. Calculate the volume of the cylinder. Give your answer correct to 3 significant figures. (Take π=3.14) Practice 2 (b) BC = 4cm, CF = 12cm, AB = 5cm and angle ABC is 90°. Calculate the volume of the triangular prism. 15cm 5cm 4cm Answer

  12. Practice 2 answer (a) Volume of cylinder = area of cross section x h V = π r² h (Take π = 3.14) V = π x r x r x h V = 3.14 x 4 x 4 x 15 V = 753.6 V = 754 cm³ (3 SF) (b) Volume of prism = area of cross section x L V = ½ x b x h x L V = ½ x 4 x 5 x 12 V = 120 cm³

  13. Practice 3A Answer (b) Calculate the volume of the silver bar.

  14. Practice 3A answer Area of cross section (trapezium) ½ (a + b) x h ½ (4 + 10) x 4 ½ x 14 x 4 28cm² Volume of silver bar 28 x 15 420cm³

  15. 8cm 10cm 2cm 6cm Practice 3B A box in the shape of a cube has sides of length 2 cm. These cube boxes are placed into a larger cuboid box with dimensions Height = 8cm Length = 10cm Width = 6cm How many cube boxes fit into the cuboid box exactly? Answer

  16. Practice 3B answer Volume of small cube V = l x w x h V = 2 x 2 x 2 V = 8cm³ Volume of large cube V = 6 x 8 x 10 V = 480 cm³ Number of small cubes in cuboid 480 ÷ 8 = 60

  17. The base of a cuboid is 10 cm by 10cm. The volume of the cuboid is 1420cm³. Find the height of the cuboid. V = l x b x h 1420 = 10 x 10 x h 1420 = 100 x h 1420 ÷ 100 = h 14.2 = h So the height of the cuboid is 14.2cm. Example h cm 10 cm 10 cm

  18. Practice 4A BC = 4cm, CF = 12 cm and angle ABC = 90°. If the volume of the triangular prism is 84 cm³. What is the length of the side AB of the prism?

  19. Practice 4A answer Volume of prism = area of cross section x length 84 = ½ x 4 x AB x 12 84 = AB x 24 84 ÷ 24 = AB AB = 3.5cm

  20. Practice 4B A cuboid has a volume of 160 cm³. Its length is 8cm and its height is 4 cm. Work out the breadth of the cuboid. Answer

  21. Practice 4B answer Volume of cuboid = l x b x h 160 = 8 x 4 x b 160 = 32 x b 160 ÷ 32 = b b = 5 cm

  22. Questions

  23. 1. (a) Christopher buys a fish tank. The dimensions of the tank are 91 cm by 32 cm by 35 cm. (i) Calculate the volume of the tank in cm³. ............................................................................................................................................................................................................................................ (ii) How many litres of water will the tank hold when full? (1000 cm³ = 1 litre) ...................................................................................................................................................................................................................................................... (2) Answers • Volume of a cuboid = l x b x h • V = 91 x 32 x 35 • V = 101920 cm³ (ii) 101920 ÷ 1000 = 101.92 litres

  24. The diagram shows a cuboid. The cuboid has a volume of 180 cm3. Calculate the height of the cuboid. .............................................................................................................................................. ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer .................................................... cm Answer Volume of a cuboid = l x b x h V = l x b x h 180 = 8 x 5 x h 180 = 40 x h 180 ÷ 40 = h 4.5 = h The height of the cuboid is 4.5cm

  25. The diagram shows a bale of straw. The bale is a cylinder with radius 70 cm and height 50 cm. Calculate the volume of the bale. State your units. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Answer ........................... (4) Answer Volume of a cylinder = area of cross section x height Area of cross section = πr² = π x 70 x 70 = π x 4900 Volume = π x 4900 x h = π x 4900 x 50 = π x 245000 = 769689.55 = 769690 cm³ = 769.69 m³

  26. The diagram is a drawing of a triangular prism. (a)Calculate the area of triangle ABC. ..................................................................................................................................................................................................................................................................................................................................................................................................... (2) (b)Calculate the volume of the prism. ..................................................................................................................................................................................................................................................................................................................................................................................................... (2) Answers Area of a triangle = ½ x base x height = ½ x 6 x 2 = ½ x 12 = 6 cm² (area of cross section) Volume of prism = Area of cross section x length V = 6 x 5 V = 30 cm³

  27. The diagram shows a ridge tent which is 3.6m long. Calculate the volume of the ridge tent. Answer Area of cross section Area of rectangle = 1.9m x 0.8m = 1.52m² Area of triangle = ½ x 1.9m x 1.6m(2.4 – 0.8) = ½ x 3.04 = 1.52m² Area cross section = 1.52 + 1.52 = 3.04m² Volume of prism = Area of cross section x length = 3.04 x3.6 = 10.944m³ 2.4m 0.8m 3.6m 1.9m

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