Question

The diameter of the moon is approximately 1/4of the diameter of the earth what fraction of the volume of the earth is the volume of the moon

Answer 1

Hello Mate!

Since its given in question that diameter if moon is ¼ of diameter if Earth.

Radius of earth = Diameter of earth / 2 __(1)

Diameter of moon = ¼ diameter of earth

4 × D of moon = D of earth.

Putting it in equation (1) we get

Radius of earth = 4 Diamter of moon / 2

Radius of earth = 2 × Diameter of moon.

Diameter of moon = 2 radius if moon

Radius of earth = 2 ( 2 × radius of moon )

R of earth = 4r of moon.

Volume of earth ( assuming it as spherical )

= 4/3 πR³
= 4/3 π(4r)³
= 4/3 π × 64r³

Volume of moon,

= 4/3 πr

Volume of earth / Volume of moon

$= \frac{4}{3} \pi \times 64{r}^{3} \div \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi \times 64{r}^{3} \times \frac{3}{4\pi} \\ = 64$

Hence Volume of Earth will be 64 times more than volum of moon.

Have great future ahead!

Answer 2

⇒ Let the diameter of the earth be d metre.

⇒ And, the diameter of moon is d/4 metre.

⇒ V1 = Volume of earth

⇒ V2 = Volume of moon

⇒ Volume of sphere = 4/3 π (r^3)

⇒ V1 = 4/3π(d/2)^3

⇒ V1 = π/6(d)^3

⇒ V2 = 4/3π(d/8)^3

⇒ V2 = π/384(d)^3

⇒ V1/V2

⇒ 1/64