A solid cube is cut into two cuboids of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboids.

Explanation

Let the side of the cube be `a`
Total surface area of a cube ` = 6a^2 `
The length of each resulting cuboid is half of the side of the cube` = a/2`
The height and breadth of the cuboid remain the same as the side of the cube a .
Total surface area of a cuboid ` = 2(lb + bh + lh) = 2 ( a/2xx a + axx a + a/2 xxa ) = 4 a^2 `
The ratio of the total surface area of the given cube and that of one of the cuboids `= 6a^2: 4a^2 = 3: 2`