A cube of side 5 cm is cut into smaller cubes of side 1 cm. What is the ratio of the total surface area of the larger cube and the sum of the total surfaces of all the smaller cubes?

Correct option is A

Given:
Large cube side = 5 cm
Small cube side = 1 cm
Formula Used:
Total Surface Area of a Cube = 6 $$\times(side)^2$$​​
Number of small cubes =​$$\frac{\text{(Large cube volume) }}{\text{ (Small cube volume)}}$$

Solution:
Number of Small Cubes:
Volume of large cube = $$5^3 = 125 cm^3$$​​
Volume of small cube =$$1^3 = 1 cm^3$$​​
Number of small cubes = $$\frac{125 }{ 1 }= 125$$​​
Total Surface Area of Large Cube:
Total surface area = $$6 \times(5^2) = 6 \times 25 = 150 cm^2$$​​
Total Surface Area of One Small Cube:
Total surface area = $$6 \times (1^2) = 6 \times 1 = 6 cm^2$$​​
Sum of Total Surface Areas of All Small Cubes:
Total surface area = $$125 \times 6 = 750 cm^2$$​​
Ratio of Total Surface Areas:
Ratio = $$\frac{\text{Total Surface Area of Large Cube}}{\text{Sum of Total Surface Areas of Small Cubes}}$$​​

Ratio =$$\frac{150 }{ 750} = \frac{1 }{ 5}$$​

Thus, option (a) is right.




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