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# SHAPE AND SPACE

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### SHAPE AND SPACE

1. 1. WAJA MATHEMATICS YEAR 6 JPN PERAK Learning Outcomes Find the volume of 3-D composite shape of two or more cubes and cuboids. 2. Solve problems in real context involving calculation of surface area and volume of 3-D shapes. 97
2. 2. WAJA MATHEMATICS YEAR 6 JPN PERAKRevision for 3 Dimensional Shapes CUBE CUBOID Volume = breadth × height × length Example question : Find the volume for this cube. Cube has same length 5 cm for every edges 5 cm 5 cm Volume = 5 cm × 5 cm × 5 cm = 125 cm³Calculate the volume for this cuboid Volume = 2 cm × 4 cm × 5 cm = 40 cm³ 98
3. 3. WAJA MATHEMATICS YEAR 6 JPN PERAKFind the volume of 3-D composite shape of two or more cubes and cuboids. Example 1 5 cm 4 cm 7 cm The composite shape is made up of a cuboid and a cube. Find the total volume of the composite shape. Recognize all the given lengths of certain sides the Step 1 : Cube : Length = 5, Breadth = 5, Height = 5 Cuboid : Volume = length Length = 7, Breadth = 5, Height = 4 × breadth × Step 2 : Find the Volume of cube = 5 × 5 × 5 = 125 cm3 volume using the formula Volume of cuboid : = 7 × 5 × 4 = 140 cm3 Step 2 : Total up the volume of cube Total Volume and cuboid = 125 cm3 + 140 cm3 = 165 cm3 99
4. 4. WAJA MATHEMATICS YEAR 6 JPN PERAK cm3 means cubic Example 2 : 6 cm The diagram is made up of three cubes. Calculate the total volume of the three cubes. Recognize all the given lengths of certain sides the Step 1 : Remember : All the dimension of cube are in the same length. Cube : Volume = length Length = 6, Breadth = 6, Height = 6 × breadth × Step 2 : Find the Volume of a cube volume using = 6 × 6 × 6 = 216 cm3 the formula Step 2 : Total up the volume of cube Solution 1 : and cuboid Total Volume : = Number of cubes × 216 cm3 Solution 2: = 216 cm3 + 216 cm3 + 216 cm3 100
5. 5. WAJA MATHEMATICS YEAR 6 JPN PERAK Don’t forget to = ? cm3 write the unit ofExercise 1 NO ITEM SOLUTIONS 1. Complete the table with the correct measurement. Length 2cm 5cm Height 10cm Breadth 2. Find the total volume of cube and cuboid shape below. 3. The figure shows a combination of two identical cubes and a cuboid 10 cm 3 cm Find the total volume of the combination. 4. 101
6. 6. WAJA MATHEMATICS YEAR 6 JPN PERAK 3 cm Calculate the total volume of the two identical cubes.Solve problems in real context involving calculation of surface area and volume of 3-D shapes. Example 1 : Diagram 4 shows a cuboid A and a cube B. 3cm 2cm cccmcm A B cm 2cm cm 10cm cm Diagram 4 What is the difference between the volumes, in cm, of A and B ? Understanding Step 1 : the problem 1. To find the difference between the volumes of 2 boxes. Devise a plan Step 2 : using formula Volume = Length × Breadth × Height for calculating volume To find the difference subtract bigger volume by smaller volume Carry out Step 3 : the plan Volume of cuboid = 10 × 2 × 3 = 60 cm³ Volume of cube = 2 × 2 × 2 = 8 cm³ Difference = 60 cm³ - 8 cm³ 102
7. 7. WAJA MATHEMATICS YEAR 6 JPN PERAK = 52 cm³Exercise 2 NO ITEM SOLUTIONS 1. Diagram 5 shows a cuboid X and cube Y. 8 cm 5 cm X Y 9 cm Diagram 5 What is the total volume, in cm3, of cuboid X and cube Y ? 2. The diagram shows a combination of cuboid A, cuboid B, and cube C. 8 cm A B C 12 cm Calculate the total volume of the diagram. 3. 5 cm 10 cm 8 cm The diagram shows three cuboids of the same size. Find the volume of the combination. 103
8. 8. WAJA MATHEMATICS YEAR 6 JPN PERAK 4. A rectangular swimming pool with a length of 10 m, width of 5 m and a height of 2 m, is completely filled with water. What is the volume of water in the swimming pool? 104