Question

The diameter of the moon is one sixth of the
diameter of the earth. Find the ratio of their
volumes (Assuming that both moon and earth are
spherical in shape).
​

Answer 1

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Both the moon and earth are in the shape of spheres.

Volume of sphere=$\large \rm\frac{4}{3} \pi {r}^{2}$

Let $\rm \: d_1$

be the diameter of moon and $\rm \: d_2$

be the diameter pf earth.

Let$\rm\: r_1$be the radius of moon and $\rm \: r_2$

be the radius of earth.

$\rm \: Given: d_1=\frac{1}{6}d_2$

$\rm \implies 2r_1 = \frac{1}{6} 2r_2 \\ \\ \rm \implies \: r_1 = \frac{1}{6} r_2$

Now the ratio of their volumes is:

$\rm \: V_1 : V_2 \\ \\ \implies \rm \frac{4}{3} \pi {r}^{3}_1 \: : \: \frac{4}{3} \pi {r}^{3} _2 \\ \\ \rm \implies \: {r}^{3} _1 : {r}^{3} _2 \\ \\ \rm \implies {1}^{3} : {6}^{3} \\ \\ \rm \implies1 : 216$

So the ratio of the volumes of the moon and the earth is 1:216

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