Question

The radius of the Moon is 1700km, and the radius of the Earth is 6350km. A scale model of the Earth and the Moon is made. In the model, the radius of the Moon is 3.4cm

(i) Find the radius of the scale model of the Earth
(ii) Find the volume of the scale model of the Earth

Answer 1

(i) The radius of the scale model of the Earth is 12.7 cm and its volume is 8580.25 cm³ (ii)

Explanation:

First you have to find the ratio between the radius of the Moon and the radius of its model (3.4 cm/1700km) and then multiply it for the radius of the Earth model.

Radius of the scale model of the Earth = 6350 km x (3.4 cm/1700 km)

⇒Radius of the scale model of the Earth = 12.7 cm.

Finally, to find the volume of the scale model of the Earth you have to use the formula for the volume of a sphere.

V= 4πr³/3 ⇒ V= 4π(12.7 cm)³/3⇒ V= 8580.25 cm³