Question

please someone give me the answer​

Answer 1

Question:-

The diameter of the moon is approximately one forth of the diameter of the earth. what fraction of the volume of the earth is the volume of the moon ?

Answer:-

Let the diameter of the earth be d

We know that,

Diameter/2 = radius

So,

d/2 = Radius of earth

Given that:

Diameter of the moon = 1/4 of earth's diameter

⟹ Diameter of the moon = d/4

⟹ Radius of the moon = (d/4)/2 = d/4 * 1/2 = d/8

We know,

Earth is in the shape of a sphere.

• Volume of a sphere = 4/3 * πr³ (r is the radius of the sphere)

Let us assume that the volume of the earth is x times the volume of moon.

⟹ 4/3 * π * (d/2)³ = x * 4/3 * π * (d/8)³

(4/3 , π are cancelled out both sides).

⟹ d³/8 = x * d³/512

⟹ d³/8 * 512/d³ = x

⟹ 64 = x

∴ The volume of earth is 64 times the volume of moon.

Answer 2

Let d 1 and d 2 be the diameters of the moon and the earth respectively.

Then, d 1

=

$\frac{1}{4} d2$

⇒

$\frac{r1}{r2} = \frac{1}{4}$We know that volume of sphere =

$\frac{4}{3} \pi \: r {}^{3}$

$\frac{volumn \: of \: moon}{volume \: of \: earth } = \frac{ \frac{4}{3} \pi \: r {1}^{3 } }{ \frac{4}{3} \pi \: r {2}^{3} } = ( \frac{r1}{r2} ) {}^{3}$

$= \frac{1}{64}$

hope this helps you

can you understand??