Let the radius of the earth be R and the radius of the moon be r
Diameter of the moon = \(\frac{1}{4}\) × diameter of the earth
The radius of the moon = \(\frac{1}{4}\) × radius of the earth
r = \(\frac{1}{4}\) × R
r = \(\frac{R}{4}\)
The volume of the earth = \(\frac{4}{3}\pi\) R3
The volume of the moon = \(\frac{4}{3}\pi\) r3
= \(\frac{4}{3}\pi\) \((\frac{R}{4})^3\)
= \(\frac{1}{64} ×\frac{ 4}{3}\)\(\pi\) R3
\(⇒\) The volume of the moon = \(\frac{1}{64}\)× Volume of the earth
Therefore, the volume of the moon is \(\frac{1}{64}\) times the volume of the earth.
(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross - streets can be referred to as (4, 3).
(ii) how many cross - streets can be referred to as (3, 4).