Three equal cubes are placed adjacently in a row. Find the ratio to total surface area on the new cuboid to that of the sum of the surface areas of the three cubes.
Answers
The ratio of total surface area of the new cuboid to the sum of surface area of the three cubes is 7 : 9 .
• Let the side of each cube be x units.
Surface area of a cube is given as : 6.(side)²
Therefore, surface area of each cube = 6.(x units)² = 6x² square units
Sum of surface area of three cubes = (6x² + 6x² + 6x²) sqaure units
= 18x² square units
• When the three cubes are joined, a cuboid is formed.
The dimensions of the cuboid are :
Length = (x + x + x) units = 3x units
Breadth = x units
Height = x units
(Refer to the image attached below for a better understanding)
• The formula for total surface area of a cuboid is given as :
2 ( lb + bh + lh ) square units
Total surface area of the new cuboid = 2 ( 3x.x + x.x + 3x.x) square units
= 2 ( 3x² + x² + 3x²) sqaure units
= 2 × 7x² square units
= 14x² sqaure units
• Now, the required ratio is given as : Total surface area of the cuboid / Sum of surface area of the three cubes
=> Ratio = 14x² square units / 18x² square units
Or, ratio = 7 / 9
Or, ratio = 7 : 9
