Question

The diameters of the moon is approximately one fourth of the turn off the earth what is the ratio of the volume of the moon to the volume of the earth

Answer 1

Answer:let diameter of earth = D

diameter of moon =D/4

=) radius of earth = D/2

=) radius of moon = D/8

earth and moon are like spheres.

so volume 0f earth = 4/3×π(D/2)^3

and volume of moon = 4/3 × π(D/8)^3

so ratio of their volumes

= 512/8 = 64:1

curved surface area of earth = 4π(D/2)^2

curved surface area of moon = 4π(D/8)^2

so ratio of their surface area

= 64/4 = 16:1

I HOPE THIS HELP U

Answer 2

Answer:

1 : 64

Step-by-step explanation:

Diameter of Moon = Diameter of Earth / 4

Let r be the radius of moon and R be the radius of Earth

⇒ 2r = 2R / 4

⇒ 4 × 2r = 2R

⇒ 8r = 2R

⇒ R = 4r

Volume of Moon = 4/3 πr³

Volume of Earth = 4/3 π(R)³

Substituting the value of R we get,

⇒ Volume of Earth = 4/3 π ( 4r )³

⇒ Volume of Earth = 4/3 π × 64r³

Now Dividing Volume of Moon / Volume of Earth we get,

⇒ 4/3 π r³ / 4/3 π ( 64 ) r³

4/3 πr³ gets cancelled and we get,

⇒ 1 / 64

Hence the ratio of volumes is 1/64 or 1 : 64

Hope it helped !!