Question 75

If the surface area of two spheres is in the ratio 49 : 25, then the ratio of their volumes will be:

Solution

Surface area of a sphere = $$4\pi R^{2}$$

Ratio of surface area of two spheres = $$\frac{4 \pi R1^{2}}{4 \pi R2^{2}} = \frac{49}{25}$$
$$\frac{R1}{R2}=\frac{7}{5}$$

Volume of a sphere = $${\frac{4}{3} \pi R^{3}}$$

Ratio of the volume = $$\frac{\frac{4}{3} \pi R1^{3}}{\frac{4}{3} \pi R2^{3}} = \frac{343}{125}$$

Option D is correct.

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