A cube of dimension 5 cm × 5 cm × 5 cm is painted red on all six faces. Now this cube is cut to form 1 cm × 1 cm × 1 cm identical cubes. What is the ratio of total area of painted surfaces to the total area of unpainted surfaces?
Explanation:
A 5 cm × 5 cm × 5 cm cube is cut into 1 cm × 1 cm × 1 cm identical cubes.
Total surface area of the original cube = 6 × (5 × 5) = 150 cm2.
Number of smaller cubes obtained = 5 × 5 × 5 = 125
Total surface area of a smaller cube = 6 × (1 × 1) = 6 cm2. Total surface area of 125 smaller cube = 125 × 6 = 750 cm2.
Now, out of 750 cm2, 150 cm2 is painted, hence the unpainted surface area = 750 - 150 = 600 cm2.
∴ Ratio of painted surface to unpainted surface = 150/600 = 1 : 4
Alternatively, To cut the given cube in to 125 (5 × 5 × 5) smaller cubes, we have to make 4 cuts in all the 3 dimensions, i.e. a total of 12 cuts.
Every cut will expose unpainted area equal to 2 faces of the original cube.
So in total area of unpainted surfaces = 24 faces of original cube
Area of painted surface = 6 surfaces of original cube
∴ Ratio of painted to unpainted surfaces = 6/24 = 1/4
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.