If the ratio of the volume of two spheres is 1 : 8, then the ratio of their surface area is:

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Question

This question was previously asked in

RRB Technician Grade III Official Paper (Held On: 30 Dec, 2024 Shift 1)

Answer 1

Given:

The ratio of the volume of two spheres is 1 : 8

Formula used:

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

Surface area of a sphere = \(4\pi r^2\)

Calculation:

Let the radii of the two spheres be \(r_1\) and \( r_2\)

\(\dfrac{V_1}{V_2}\) = \(\dfrac{4}{3}\pi r_1^3\) / \(\dfrac{4}{3}\pi r_2^3\) = \(\dfrac{r_1^3}{r_2^3} = \dfrac{1}{8}\)

⇒ \(\left(\dfrac{r_1}{r_2}\right)^3 = \dfrac{1}{8} \)

⇒ \(\dfrac{r_1}{r_2} = \dfrac{1}{2}\)

The ratio of their surface areas is:

\(\dfrac{S_1}{S_2} = \dfrac{r_1^2}{r_2^2}\)

⇒ \(\left(\dfrac{r_1}{r_2}\right)^2 = \left(\dfrac{1}{2}\right)^2 = \dfrac{1}{4}\)

∴ The correct answer is option (1).

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