If the ratio of volumes of two sphere is 1 ∶ 8, the ratio of their surface area is-

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If the ratio of volumes of two sphere is 1 ∶ 8, the ratio of their surface area is-

This question was previously asked in

OSSSC RI/ ARI/ Amin (Mathematics) 2015 Official Paper-II (Held On: 7th Feb 2016)

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1 ∶ 2
1 ∶ 4
1 ∶ 8
1 ∶ 16

Answer 1

Given:

- The ratio of volumes of two spheres is 1 : 8

Solution:

⇒ The volume of a sphere is given by the formula

\frac{4}{3} π r^{3}

$\frac{4}{3} \pi r^3$ , and the surface area is given by

4 π r^{2}

$4 \pi r^2$ .

⇒ If the ratio of the volumes of two spheres is 1 : 8, then the ratio of their radii is the cube root of that, or 1 : 2, because the volume is proportional to the cube of the radius.

⇒ The surface area of a sphere is proportional to the square of the radius, so if the ratio of the radii is 1 : 2, then the ratio of the surface areas is the square of that, or 1 : 4.

∴ The correct option is 2) 1 : 4.

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If the ratio of volumes of two sphere is 1 ∶ 8, the ratio of their surface area is-

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