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 r³

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 R³

The volume of the moon = 4/3π r³

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

= 1/64 × 4/3π R³

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.

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

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.

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