Question:
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
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Cutting a side-4 cube into unit cubes multiplies the total surface area by exactly 4, a 300% increase.
Updated On: Jul 15, 2026
- 4%
- 300%
- 75%
- 400%
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The Correct Option is B
Solution and Explanation
Step 1: Find the original surface area.
Surface area of a cube \(=6\times(\text{side})^2=6\times4^2=6\times16=96\) cm².
Step 2: Find the number of small cubes.
Number of 1 cm cubes \(=\dfrac{\text{volume of big cube}}{\text{volume of small cube}}=\dfrac{4\times4\times4}{1\times1\times1}=64\).
Step 3: Find the total surface area of the small cubes.
Surface area of each small cube \(=6\times1^2=6\) cm². Total \(=64\times6=384\) cm².
Step 4: Find the percentage increase.
Increase \(=384-96=288\) cm². Percentage increase \(=\dfrac{288}{96}\times100=300\%\).
Step 5: Final Answer.
The surface area increases by 300%, so option B is correct.
Surface area of a cube \(=6\times(\text{side})^2=6\times4^2=6\times16=96\) cm².
Step 2: Find the number of small cubes.
Number of 1 cm cubes \(=\dfrac{\text{volume of big cube}}{\text{volume of small cube}}=\dfrac{4\times4\times4}{1\times1\times1}=64\).
Step 3: Find the total surface area of the small cubes.
Surface area of each small cube \(=6\times1^2=6\) cm². Total \(=64\times6=384\) cm².
Step 4: Find the percentage increase.
Increase \(=384-96=288\) cm². Percentage increase \(=\dfrac{288}{96}\times100=300\%\).
Step 5: Final Answer.
The surface area increases by 300%, so option B is correct.
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