The diameter of the moon is approximately one | vedclass

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Question

(A) Let the radius of the earth be $R$ and the radius of the moon be $r$.Given that the diameter of the moon is $\frac{1}{4}$ of the diameter of the e

Vedclass · Accepted Answer

$\frac{1}{64}$

Vedclass · Answer

(A) Let the radius of the earth be $R$ and the radius of the moon be $r$.Given that the diameter of the moon is $\frac{1}{4}$ of the diameter of the earth,it follows that the radius of the moon is $\frac{1}{4}$ of the radius of the earth,i.e.,$r = \frac{R}{4}$.The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Volume of the earth $(V_E)$ $= \frac{4}{3} \pi R^3$.Volume of the moon $(V_M)$ $= \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \left(\frac{R}{4}\right)^3 = \frac{4}{3} \pi \left(\frac{R^3}{64}\right) = \frac{1}{64} \left(\frac{4}{3} \pi R^3\right)$.Therefore,$V_M = \frac{1}{64} V_E$.The fraction of the volume of the earth that is the volume of the moon is $\frac{V_M}{V_E} = \frac{1}{64}$.

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

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