3D Shapes and Nets PDF Past Paper

11 3D shapes 11.1 Shapes and nets compound shape Worked example 1 prism surface area Describe this compound shape. This compound shape is made from a Think how you can s...

11 3D shapes 11.1 Shapes and nets compound shape Worked example 1 prism surface area Describe this compound shape. This compound shape is made from a Think how you can split the compound cone and a cylinder. shape into simpler 3D shapes that you know. 119  11 3D shapes Exercise 11.1 Focus 1 Complete these descriptions of compound shapes. a This compound shape is made from a and a. b This compound shape is made from two. c This compound shape is made from a and a. 2 The diagram shows four shapes A, B, C and D. It also shows four sketches of nets i, ii, iii and iv. A B C D i ii iii iv Draw a line to match each shape to the correct net. 120  11.1 Shapes and nets 3 Write down the smallest number of unit cubes that must be added to these shapes to make cuboids. a b c Practice 4 Sketch a compound shape that is made from these simple shapes. a three different cuboids 121  11 3D shapes b two identical cones c two identical pyramids. 5 Describe and sketch a net of these shapes. a triangular prism 122  11.1 Shapes and nets b hexagonal prism. 6 Describe how could you work out the surface area of the shapes in question 5. 7 Write down the smallest number of unit cubes that must be added to these shapes to make cuboids. a b c 123  11 3D shapes Challenge 8 Sketch a net for these shapes. a b 124  11.1 Shapes and nets 9 Write down the smallest number of unit cubes that must be added to these shapes to make cubes. a b c 125  11 3D shapes 10 These two shapes are made from unit cubes. Fran takes the shapes apart and uses all the unit cubes to make a cuboid. Draw a sketch to show two different cuboids she can make with all the cubes. Use isometric paper if you have some. 126  11.2 Capacity and volume 11.2 Capacity and volume Worked example 2 capacity volume The diagram shows some water in a jug. ml 500 400 300 200 100 0 a What is the capacity of the jug? b What is the volume of water in the jug? a 500 ml 500 ml is the maximum the jug can hold b 300 ml The scale shows the water is at the 300 ml mark. Exercise 11.2 Focus 1 For each of these jugs write down i the capacity of the jug ii the volume of water in the jug. a b ml 100 c ml 500 ml 5000 90 4500 400 80 4000 70 60 3500 300 50 3000 40 2500 200 30 2000 20 1500 100 10 1000 500 i ii 127  11 3D shapes 2 Write the capacity of the container and the volume of the liquid for each of these diagrams. A litres 2 1.75 1.5 1.25 1 0.75 0.5 0.25 Capacity Volume B ml 200 180 160 140 120 100 80 60 40 20 Capacity Volume C litre 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Capacity Volume D ml 1600 1400 1200 1000 800 600 400 200 Capacity Volume E litres 1.2 1 0.8 0.6 0.4 0.2 Capacity Volume 128  11.2 Capacity and volume 3 Show how these bottles should be organised and grouped in the Venn diagram. Bottle A Bottle B Bottle C Bottle D 0.09 litres 300 ml 200 ml 75 ml 400 ml 750 ml 500 ml 1 litres Bottle E Bottle F Bottle G Bottle H 80 ml 0.2 litres 0.5 litres 50 ml 300 ml 80 ml 0.2 litres 0.75 litres Capacity less Volume less than 500 ml than 100 ml Draw one more bottle in each of the four sections of the Venn diagram. Label the bottles with their capacity and the volume of liquid inside. 129  11 3D shapes 4 Complete this table. Remember that 1000 ml = 1 litre. millilitres litres and millilitres litres 4100 ml 4 l 100 ml 4.1 l 1500 ml 1l ml 3 l 600 ml 2.5 l 400 ml 0 l 400 ml 9600 ml 5 What number is the arrow pointing to on each of these scales? Look at the tip boxes for help. a 200 ml Tip There are four spaces for an increase 100 ml of 100 ml, so each increment is worth 100 ÷ 4 = 25 ml. b 400 ml Tip There are five spaces for an increase 300 ml of 100 ml, so each increment is worth 100 ÷ 5 = 20 ml. c 3l Tip There are five spaces for an increase 2l of 1 l, so each increment is worth 1 ÷ 5 = 0.2 l. 130  11.2 Capacity and volume Practice ml 100 90 6 Zara and Sofia are looking at this question. 80 70 What is the volume of water in this jug? 60 50 Read what they say. 40 30 20 10 I think the volume of water is 79 ml. I think the volume of water is 78 ml. a Who is correct? Explain why. b Explain the mistake that the other person has made. c What volume of water must be added to the jug to fill it to capacity? 131  11 3D shapes 7 For each of these jugs write down: i the capacity of the jug ii the volume of water in the jug. a b c ml 200 litres 4 ml 800 600 100 3 400 2 200 1 i ii 8 What volume of water must be added to the jugs in question 7 to fill them to capacity? a b c 9 a What is the total capacity of the 5 cans of oil below? litres A B C D E 2.5 litres 2.5 litres 2.5 litres 2.5 litres 2.5 litres b Estimate the volume of oil needed to fill each can. Give your answers in millilitres. a b c d e 132  11.2 Capacity and volume Challenge 10 Dakarai needs 3 litres of water. He only has the water shown in the measuring jugs. litres 3 litres 1.8 2 1.2 1 0.6 Does he have enough water? Explain your answer. 11 Rhian has a bucket with a capacity of 10 litres. 3 The bucket is full of water. 5 1 Wyn has a bucket which is full of water. 3 He has the same volume of water in his bucket as Rhian. What is the capacity of Wyn’s bucket? 12 Elin has these four measuring cups, A, B, C and D. The capacity of each cup, in millilitres, is shown. 240 ml 160 ml 120 ml 60 ml A B C D 133  11 3D shapes Explain how Elin can use the cups to accurately measure out these volumes: a 40 ml b 180 ml c 80 ml d 100 ml e 20 ml 13 Jenny was asked this question: Is the capacity of a container always greater than the volume of the liquid inside? Jenny wrote: The capacity of a container must always be greater than the volume of the liquid inside because the capacity is the maximum the container can hold. Think carefully about capacity, volume and Jenny’s answer. Write an improved answer of your own. 134