The surface area of a cube is increased by 25%. If p is the percentage increase in its length, then which one of the following is correct ?  

This question was previously asked in
CDS Elementary Mathematics 16 April 2023 Official Paper
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  1. 16 < p < 18 
  2. 14 < p < 16 
  3. 12 < p < 14 
  4. 10 < p < 12 

Answer (Detailed Solution Below)

Option 4 : 10 < p < 12 
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Detailed Solution

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Formula used:

The area of each surface of the cube = (side)2  [each surface of a cube is a square]

Calculation:

Let the initial surface area of the cube = 600

then the initial area of each surface = 100 

Initial length of side = √100 = 10 unit

Final Surface area of the cube = 600 × 125/100 = 750

Then the final area of each surface = 125

(Final length)2 = 125

(Final length) = √125 

Therefore, according to the question

P = [(√125 - 10)/10] × 100 

P = 10(5√5 - 10) 

P = 10(5 × 2.236 - 10) = 11.8

∴ 10 < P < 12

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