Question:
If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
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For any 2D area proportional to the square of a linear dimension, if the linear dimension scales by a factor \(k\), the area scales by \(k^2\). Here, \(k = 1.5\), so the area scales by \(1.5^2 = 2.25\), which is a \(125%\) increase.
Updated On: May 9, 2026
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The problem asks for the percentage change in the surface area of a cube when its side length is increased by a specific percentage.
Step 2: Key Formula or Approach:
The total surface area (\(S\)) of a cube with edge length \(a\) is given by \(S = 6a^2\).
Percentage increase is calculated as \(\frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \times 100%\).
Step 3: Detailed Explanation:
Let the original edge of the cube be \(a\).
The original surface area is \(S_1 = 6a^2\).
The new edge length after a \(50%\) increase is: \[ a' = a + 0.5a = 1.5a \] The new surface area is: \[ S_2 = 6(a')^2 = 6(1.5a)^2 \] \[ S_2 = 6(2.25a^2) = 2.25(6a^2) = 2.25 S_1 \] The increase in surface area is: \[ \Delta S = S_2 - S_1 = 2.25 S_1 - 1 S_1 = 1.25 S_1 \] The percentage increase is: \[ \text{Percentage Increase} = \left( \frac{1.25 S_1}{S_1} \right) \times 100% = 125% \]
Step 4: Final Answer:
The percentage increase in its surface area is \(125%\).
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