Volume of a sphere is equal to the volume of a hemisphere. Find the ratio of their radius.

  1. 1 : √3
  2. 1 : √2
  3. 1 : \(\sqrt[3]{4}\)
  4. 1 : \(\sqrt[3]{2}\)

Answer (Detailed Solution Below)

Option 4 : 1 : \(\sqrt[3]{2}\)
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Formula:

Volume of sphere = [4/3] × πr3

Volume of hemisphere = [2/3] × πr3

Calculation:

Let the radius of sphere and hemisphere be R and r respectively, then

According to the question

[4/3] × π × R3 = [2/3] × π × r3

⇒ R3/r3 = 1/2

⇒ R : r = 1 : ∛2

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