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# 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? - CBSE Class 9 - Mathematics

ConceptVolume of a Sphere

#### Question

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 1

Let the diameter of earth be d. Therefore, the radius of earth will be d/2.

Diameter of moon will be d/4 and the radius of moon will be d/8.

"Volume of moon "=4/3pir^3=4/3pi(d/8)^3=1/512xx4/3pid^3

"Volume of earth "=4/3pi^3=4/3pi(d/2)^3=1/8xx4/3pid^3

"Volume of moon"/"Volume of earth"=(1/512xx4/3pid^3)/(1/8xx4/3pid^3)=1/64

rArr "Volume of moon "=1/64"Volume of earth"

Therefore, the volume of moon is 1/64 of the volume of earth.

#### Solution 2

Given that,
The diameter of the moon is approximately one fourth of the diameter of the earth.

Let diameter of earth bed. So radius =d/2

Then, diameter of moon=d/4,radius =2/4=d/8

Volume of moon =4/3πr^3=4/3π(d/8)^3=4/3xx1/512πd^3

Volume of earth =4/3πr^3=4/3π(d/2)^3=1/8xx4/3πd^3

"Volume of moon"/"Volume of earth"=(1/512xx4/3πd^3)/(1/8xx4/3πd^3)=1/64

Thus, the volume of moon is 1/64of volume of earth.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 21: Surface Areas and Volume of a Sphere
Ex.21.20 | Q: 24 | Page no. 21
NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex.13.80 | Q: 4 | Page no. 236
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? Concept: Volume of a Sphere.
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