Question

Three identical cubes are placed adjacent to each other to form a cuboid. Find the ratio of surface area of the cuboid to the sum of the total surface areas of three cubes.

Answer 1

let the side off cube be 'a'
total surface area of cube = 6a²
length of cuboid = 3a
breadth of cuboid = a
height of cuboid = a
total surface area of cuboid = 2( 3a × a + a × a + a × 3a ) = 14a²
ratio = 14a²/6a² = 7/3 = 7 : 3

Answer 2

Answer: The ratio of surface area of the cuboid to the sum of the total surface areas of three cubes is 7:9 .

• The surface area of a cube of side 'a' = 6a² .

• The sum of surface area of three cubes of side 'a' = 3x6a²= 18a²

• The legnth, breadth and height of the new cuboid formed by joining three cubes of side 'a' are 3a, a, and a.

• The surface area of cuboid = 2( 3axa + axa + ax3a ) = 14a².

• The ratio of surface area of the cuboid to the sum of the total surface areas of three cubes = 14a²:18a² = 7:9.

Thus the required ratio is 7:9.