Question

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 .

Answer 1

Let the Diameter of the Earth be : E

⇒ Radius of the Earth : E/2

Given the Diameter of the Moon is one - fourth of the Diameter of the Earth

⇒ Diameter of the Moon : 1/4 × E = E/4

⇒ Radius of Moon : E/8

Assuming the Shape of Both Moon and Earth as Sphere

We know that the Volume of a Sphere is given by 4/3 × π × r³

where 'r' is the radius of the Sphere

⇒ Volume of Earth = 4/3 × π × (E/2)³ = 4/3 × π × E³/8

⇒ Volume of Moon = 4/3 × π × (E/8)³ = 4/3 × π × E³/8 × 1/64

But (4/3 × π × E³/8) is the Volume of Earth

⇒ Volume of Moon = (Volume of Earth)/64

So, 1/64 Fraction of the Volume of the Earth is the Volume of the Moon