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The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area. - CBSE Class 9 - Mathematics

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Question

The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.

Solution

Let the diameter of earth be d. Therefore, the diameter of moon will be d/4.

Radius of earth = d/2

`"Radius of moon "= 1/2xxd/4 = d/8`

`"Surface area of moon "= 4pi(d/8)^2`

`"Surface area of earth "= 4pi(d/2)^2`

`"Required ratio "=(4pi(d/8)^2)/(4pi(d/2)^2)=4/64=1/16`

Therefore, the ratio between their surface areas will be 1:16.

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APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 13: Surface Area and Volumes
Ex. 13.40 | Q: 7 | Page no. 225

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Solution The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area. Concept: Surface Area of a Sphere.
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