If the surface area of a sphere S₁ is 800% greater than that of sphere S₂, and the volume of sphere S₂ is x% lower than sphere S₁, then ‘x’ in terms of percentage is: (Rounded off to two places of decimals)

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 31 Jan 2023 Shift 1)

Answer 1

Calculation:

As per question,

⇒ Surface Area of S1 : Surface Area of S2 = 9 : 1

⇒ 4πR² : 4πr2 = 9 : 1

⇒ R : r = 3 : 1

⇒ Volume of S1 : Volume of S2 = R³ : r³

⇒ Volume of S1 : Volume of S2 = 3³ : 1³

⇒ Volume of S1 : Volume of S2 = 27 : 1

Percentage by which volume of S2 is lower than S1 = x %

x% = [(27 -1)/27] × 100 = (26/27) × 100 ≈ 96.29%

∴ The correct answer is Option (3).

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