If the radius of a sphere is tripled, what is the ratio of the volume of the original sphere to that of the new sphere?

Question

Question

This question was previously asked in

SSC GD Constable 2025 Official Paper (Held On: 04 Feb, 2025 Shift 3)

Answer 1

Given:

The radius of the original sphere = r

The radius of the new sphere = 3r

Formula Used:

Volume of a sphere = \(\frac{4}{3}\pi r^3\)

Calculation:

Volume of the original sphere = \(\frac{4}{3}\pi r^3\)

Volume of the new sphere = \(\frac{4}{3}\pi (3r)^3\)

⇒ Volume of the new sphere = \(\frac{4}{3}\pi (27r^3)\)

⇒ Volume of the new sphere = \(27 × \frac{4}{3}\pi r^3\)

⇒ Volume of the new sphere = 27 × Volume of the original sphere

Ratio of the volume of the original sphere to the new sphere = 1 : 27

The correct answer is option 2.

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