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

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1 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

2 Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³ 6 cm 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 Note that there are 3 dimensions so the units are cubic m or cm.

3 Practice 1 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 Answer

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

5 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

6 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

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

8 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

9 Practice 2 (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) (b) BC = 4cm, CF = 12cm, AB = 5cm and angle ABC is 90. Calculate the volume of the triangular prism. 15cm 5cm 4cm Answer

10 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 = 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

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

12 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 cm³

13 Practice 3B A box in the shape of a cube has sides of length 2 cm. 8cm 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? 2cm 10cm 6cm Answer

14 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 = 60

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

16 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?

17 Practice 4A answer Volume of prism = area of cross section x length 84 = ½ x 4 x AB x = AB x = AB AB = 3.5cm

18 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

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

20 Questions

21 1. (a) Christopher buys a fish tank. The dimensions of the tank are 91 cm by 32 cm by 35 cm. Answers 3 5 c m 9 1 c m 3 2 c m (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) (i) Volume of a cuboid = l x b x h V = 91 x 32 x 35 V = cm³ (ii) = litres

22 The diagram shows a cuboid. Answer Volume of a cuboid = l x b x h 8 c m 5 c m H e ig h t N o t to s c a le The cuboid has a volume of 180 cm3. Calculate the height of the cuboid Answer... cm V = l x b x h 180 = 8 x 5 x h 180 = 40 x h = h 4.5 = h The height of the cuboid is 4.5cm

23 The diagram shows a bale of straw. The bale is a cylinder with radius 70 cm and height 50 cm. 7 0 c m 5 0 c m N o t to s c a le 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 = = cm³ = m³

24 The diagram is a drawing of a triangular prism. Answers A D 2 c m 5 c m B 6 c m C (a) (2) (b) (2) Calculate the area of triangle ABC Calculate the volume of the prism 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

25 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( ) = ½ x 3.04 = 1.52m² Area cross section = = 3.04m² 0.8m 1.9m 2.4m 3.6m Volume of prism = Area of cross section x length = 3.04 x3.6 = m³