Answer: 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.
