The length of the side of a cube is 4.2 cm. What is the volume of the largest sphere that can be taken out of the cube?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 2)
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  1. 26.40 cm3
  2. 20.50 cm3
  3. 38.80 cm3
  4. 48.60 cm3

Answer (Detailed Solution Below)

Option 3 : 38.80 cm3
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Detailed Solution

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Given:

The length of the side of a cube is 4.2 cm. 

Concept used:

1. The diameter of the largest sphere that can be taken out of the cube should be equal to the measure of each side of the cube.

2. Volume of a sphere = 4π(Radius)3 ÷ 3

Calculation:

Diameter of the sphere = 4.2 cm3

Radius of the sphere = 4.2/2 = 2.1 cm3

Now, the volume of the sphere

⇒ (4π × 2.13)/3

⇒ 38.808 ≈ 38.80 cm3

∴ The volume of the sphere that can be taken out of the cube is 38.80 cm3.

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