Stefan makes a cuboid that is 5 cm longer, 5 cm taller and 5 cm wider than Amina's cuboid. What is the difference between the number of cubes in Amina's and Stefan's cuboids? animas cuboid is 4x6x3

Stephan's cuboid has 90 cubes more than that of Amina

Step-by-step explanation: As stated in the question, Amina's cuboid has dimensions given as 4 cm by 6 cm by 3 cm. That means Amina's cuboid has a total volume of

Volume = L x W x H

Volume = 4 x 6 x 3

Volume = 72 cm³

A cube by standard has the length, width and height all measuring the same. This means, the in a cuboid with a volume of 72 cubic centimetres, you can find a cube with each side measuring 2 centimetres as follows;

Volume of cube = 2 x 2 x 2

Volume of cube = 8 cm³

Therefore,

Number of cubes = Volume of cuboid / Volume of cube

Number of cubes = 72/8

Number of cubes = 9

However, Stephan's cuboid now has each side measuring 5 centimetres more than each side of Amina's cuboid, hence Stephan's cuboid has the following dimensions,

L = 9 (4 + 5)

W = 11 ( 6 + 5)

H = 8 (3 + 5)

The volume of Stephan's cuboid therefore is derived as,

Volume = L x W x H

Volume = 9 x 11 x 8

Volume = 792 cm³

The number of cubes (with each side measuring 2 cm) in Stephan's cuboid is now derived as;

Number of cubes = Volume of cuboid / Volume of cube

Number of cubes = 792/8

Number of cubes = 99

From the results derived above, Stephan's cuboid has 99 cubes while Amina's cuboid has 9 cubes. The difference between both is 90 cubes.

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