Question

The radius of the Moon is 1700 km, and the radius of the Earth is 6350 km. A scale model of the Earth and the Moon is made. In the model, the radius of the Moon is 3.4 cm. (i) Find the radius of the scale model of the Earth. (ii) Find the volume of the scale model of the Earth.

Answer 1

1) 12.7 cm

2) 8580.24 cm³

Explanation:

given,

Radius of moon(Rm) = 1700 Km Radius of Earth(Re) = 6350 km

Model radius of Moon(Mm) = 3.4 cm

2) Volume of earth model =
`((R_e)^3)/((R_m)^3)* (4)/(3)\pi (M_m)^3`

=
`((6350)^3)/((1700)^3)* (4)/(3)\pi (3.4)^3`

= 8580.24 cm³

1) radius of earth =
`(R_e)/(R_m)* M_m`

=
`(6350)/(1700)* 3.4`

= 12.7 cm