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Volume of two spheres are in the ratio $64 : 27$ . The ratio of their surface areas is

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3 : 4

4 : 3

9 : 16

16 : 9

answer is D.

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Detailed Solution

Given that the volume of two spheres are in the ratio 64: 27.

\Rightarrow \frac{V_{1}}{V_{2}} = \frac{64}{27}

[

V_{1}, V_{2}

be the volumes of two spheres]
The formula for the volume of sphere is given by,
Volume of a sphere

= 43 π r 3

, where r is the radius. So, after substituting the value of all the dimensions in the formula we get,

\Rightarrow \frac{\frac{4}{3} π r_{1}^{3}}{\frac{4}{3} π r_{2}^{3}} = \frac{64}{27}

[

r_{1}, r_{2}

be the radii of two spheres]

\Rightarrow {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{4}{3})}^{3}

\Rightarrow \frac{r_{1}}{r_{2}} = \frac{4}{3}

Now, the ratio of their surface areas is given by,

(T . S . A 1) (T . S . A 2) = (4 π r 12) (4 π r 22) ⇒ (T . S . A 1) (T . S . A 2) = r 1 r 2 2

⇒ (T . S . A 1) (T . S . A 2) = 432 ⇒ (T . S . A 1) (T . S . A 2) = 169

Therefore, the ratio of their surface areas is

16 : 9

.
Hence option (4) is correct.

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