# 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?

**Solution:**

The volume of a sphere of base radius r is 4/3π r^{3}

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

Diameter of the moon = 1/4 × diameter of the earth

The radius of the moon = 1/4 × radius of the earth [Since, diameter = 2 × Radius]

r = 1/4 × R

r = R/4

The volume of the earth = 4/3π R^{3}

The volume of the moon = 4/3π r^{3}

= 4/3π (R/4)^{3} [ replacing r with R/4 ]

= 1/64 × 4/3π R^{3}

The volume of the moon = 1/64 × Volume of the earth

Hence the volume of the moon is 1/64 times the volume of the earth.

**Video Solution:**

## 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?

### NCERT Solutions for Class 9 Maths - Chapter 13 Exercise 13.8 Question 4:

**Summary:**

It is given that the diameter of the moon is approximately one-fourth of the diameter of the earth. We have found that the volume of the moon is 1/64 the fraction of the volume of the earth.