Edmund makes a cube using eight small cubes. Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund's cube. How many more cubes does Samuel use than Edmund?

Question

Mathematics

Jesus Mitchell

1 September, 05:45

Edmund makes a cube using eight small cubes. Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund's cube. How many more cubes does Samuel use than Edmund?

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Answers (1)

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Antony Anthony · Answer 1

Step-by-step explanation:

The number of small cubes that Edmund used is 8. Let us assume that the volume of each small cube is 1m³. This means that the volume of the cube made is 8m³. Since volume of cube = s³, then s = 3√8 = 2m

Each side of the cube made is 2m

Samuel uses cubes of the same size as the small cubes to make a cuboid twice as long, three times as wide and four times as high as Edmund's cube. It means that the sides of the cuboid are

Length = 2 * 2 = 4m

Width = 3 * 2 = 6m

Height = 4 * 2 = 8m

Volume = length * width * height

Volume = 4 * 6 * 8 = 192 m³

Number of small cubes used is 192/1 { = 192

The number of cubes that Samuel used more that Edmund is 192 - 8 = 184 small cubes