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If W1 and W2 are weights of two solid iron balls of radii $\frac{1}{2}$ metre and $\frac{1}{3}$ metre respectively, then which one of the following is equal to W₁ : W₂ ?

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EPFO AO EO 2021

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8 : 27

27 : 8

4 : 16

16 : 4

Explanation:

To find the ratio W1 : W2 of the weights of the two solid iron balls, we relate their weights to their volumes since they are made from the same material.

1. The volume V of a sphere is V = 4/3 pi r³

2. The radii of the two spheres are given as 1/2 metre and 1/3 metre.

3. The ratio W1 : W2 = V1 : V2 = {1/8}/{1/27} = 27 : 8

Option 2: 27 : 8 is the correct ratio.