Question

The diagram shows a solid metal cuboid.
The areas of three of the faces are marked on
the diagram.
The lengths, in cm, of the edges of the cuboid
are whole numbers.
The metal cuboid is melted and made into cubes.
Each of the cubes has sides of length 2.5 cm.
Work out the greatest number of these cubes that can be made.
You must show your working.

Answer 1

Answer:

6 cubes

Step-by-step explanation:

Considering the given cuboid, it can be deduced that;

length of the cuboid = 7 cm

width of the cuboid = 3 cm

height of the cuboid = 5 cm

Thus,

volume of the cuboid = length x width x height

                                    = 7 x 3 x 5

                                    = 105 cubic centimetres

The cubes has sides of length 2.5 cm.

volume of each cube = length x width x height

                                    = 2.5 x 2.5 x 2.5

                                    = 15.625 cubic centimetres

The greatest number of cubes that can be made = $\frac{105}{15.625}$

                                              = 6.72

The greatest number of cubes that can be made from the cuboid is 6.