Question

A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?

Answer 1

Surface area of a cube = 6a², where a is side of a cube.

.^.. Side of cube = 5 cm

.^.. Surface area of the cube = 6 × (5)² = 6 × 25 = 150 cm²

Now, surface area of the cube with side 1 cm = 6 × (1)² = 6 cm²

.^.. Surface area of 5 cubes with side 1 cm = 5 × 6 = 30 cm²

Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes

= `30/150`

= `3/15`

= 1 : 5