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SSC CHSL 2022 PYQ — Question 61

SSC CHSL - 25 May 2022 - Shift 1 • Quantitative Aptitude • Q61

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A sphere passes through the eight corners of a cube of side 14 cm. Find the volume (in cm3) of the sphere. Take π = 22/7

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 43123\sqrt{3}

If the sphere passes through the corners of the cube, then the diagonal of the cube must be the diameter of the cube.

Diagonal of the cube with side 14 cm = 143\sqrt{3}

Thus, the diameter of the sphere =  143\sqrt{3}

The volume of the sphere = (4/3) × π × r3

⇒ (4/3) × (22/7) × ( 73\sqrt{3})3 =   43123\sqrt{3}