Question

Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.

Answer 1

Let the side of a cube be 'a' units.

The total surface area of one cube = 6a²

The total surface area of 3 cubes  = 3 x 6a² = 18a²

After joining 3 cubes in a row, length of Cuboid = 3a

Breadth and height of cuboid = a

The total surface area of the cuboid  = 2( 3a² + a² +  3a² ) = 14a²

The ratio of total surface area of a cuboid to the total surface area of 3 cubes = `(14a^2) /(18a^2) = 7/9`