If the ratio of the volume of two spheres is 1 : 8, then the ratio of their surface area is:  

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RRB Technician Grade III Official Paper (Held On: 30 Dec, 2024 Shift 1)
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  1. 1 : 4
  2. 1 : 2
  3. 1 : 8
  4. 1 : 6

Answer (Detailed Solution Below)

Option 1 : 1 : 4
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Detailed Solution

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Given:

The ratio of the volume of two spheres is 1 : 8

Formula used:

Volume of a sphere = 

Surface area of a sphere = 

Calculation:

Let the radii of the two spheres be  and 

 =  /  = 

⇒ 

⇒ 

The ratio of their surface areas is:

⇒ 

∴ The correct answer is option (1).

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