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Volume · cuboid made of small cubes
P6 · Volume · PSLE Maths
Question
Mei Ling used 240 small cubes of edge 2 cm to build a solid cuboid with no gaps. The cuboid was 24 cm long and 10 cm high. What was its width? What was the volume of the cuboid?
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Hint
First change 24 cm and 10 cm into numbers of small cubes. Then find how many small cubes are in one layer.
Show the answer and step-by-step explanation
Answer: Width 8 cm; Volume 1920 cm³
- Small cube — Each small cube has edge 2 cm. First, change the cuboid's lengths into numbers of small cubes.
- Change to units — Length: 24 ÷ 2 = 12, so there are 12 small cubes along the length. Height: 10 ÷ 2 = 5, so there are 5 layers.
- One layer — There are 5 layers, and the 240 small cubes are shared equally among the 5 layers. So each layer has 240 ÷ 5 = 48 small cubes.
- Draw a layer — One layer is a rectangle. There are 12 cubes along the length and 48 cubes in the whole layer. The number along the width is 48 ÷ 12 = 4.
- Find width — There are 4 small cubes along the width, and each is 2 cm long. Width = 4 × 2 = 8 cm.
- Find volume — The volume of each small cube is 2 × 2 × 2 = 8 cm³. There are 240 small cubes, so the volume = 240 × 8 = 1920 cm³. 📌 Key idea: first change lengths into numbers of small cubes, then use total number = length count × width count × height count. The volume can also be found by number of cubes × volume of each small cube.
Method: For small cubes of edge 2 cm, number of cubes along an edge = length of the edge ÷ 2. Total number of cubes = number along length × number along width × number along height.
Practice: 3 similar questions
- Raju used 150 small cubes of edge 2 cm to build a solid cuboid with no gaps. The cuboid was 20 cm long and 6 cm high. What was its width? What was its volume?
Answer
10 cm, 1200 cm³ — Along the length: 20 ÷ 2 = 10 cubes; along the height: 6 ÷ 2 = 3 layers. Number along the width = 150 ÷ 10 ÷ 3 = 5 cubes. Width = 5 × 2 = 10 cm. Volume = 150 × 2 × 2 × 2 = 1200 cm³.
- Siti used 320 small cubes of edge 2 cm to make a cuboid display stand. The stand was 16 cm wide and 10 cm high. What was its length? What was its volume?
Answer
16 cm, 2560 cm³ — Along the width: 16 ÷ 2 = 8 cubes; along the height: 10 ÷ 2 = 5 layers. Number along the length = 320 ÷ 8 ÷ 5 = 8 cubes. Length = 8 × 2 = 16 cm. Volume = 320 × 8 = 2560 cm³.
- Ali had 500 small cubes of edge 2 cm. He used some of them to build a solid cuboid with no gaps. The cuboid was 20 cm long and 16 cm wide, and he had 100 small cubes left. What was the height of the cuboid? What was its volume?
Answer
10 cm, 3200 cm³ — He used 500 − 100 = 400 small cubes. Along the length: 20 ÷ 2 = 10 cubes; along the width: 16 ÷ 2 = 8 cubes. Number along the height = 400 ÷ 10 ÷ 8 = 5 layers. Height = 5 × 2 = 10 cm. Volume = 400 × 8 = 3200 cm³.
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