Question

The diameter of moon is approximately one – fourth of the diameter of earth. What fraction of the

volume of the earth is the volume of the moon?​

Answer 1

Let $d_1\:and\:d_2$ be the diameters of the moon and the earth respectively.

Then,$d_1=\frac{1}{4}d_2$

we know that,

volume of sphere = $\frac{4}{3} \pi {r}^{3}$

$\sf \frac{vol. \: of \: earth}{vol. \: of \: moon} = \frac{ \frac{4}{3} \pi {r}_1^{3} }{ \frac{4}{3}\pi {r}^{3}_2 }$

$\sf = { \huge( \small\frac{r_1}{r_2} \huge)}^{3}$

$\sf= {(\frac{ \frac{1}{4} r_2}{r_2}) }^{3}$

$\sf\huge( \small { \frac{1}{4} \huge)}^{3} = \frac{1}{64}$

Answer 2

Answer:

1/64

Step-by-step explanation:

Let diameter of earth =x

So, diameter of moon =  x/4

Hence,

Radius of earth =  x/2

And Radius of moon =  1/2 × x/4=x/8

Now,

Volume of earth                   4/3 π(Radius of moon)3    

                                        =

Volume of moon                   4/3  π(Radiusofearth)3

                                               π(Radius of moon)  3

                                        =          

                                                  π(Radius of earth)3

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