Question

6.
The diameter of the moon is one sixth of the
diameter of the earth. Find the ratio of their
volumes (Assuming that both moon and earth are
spherical in shape).
[2]​

Answer 1

Answer:

1:16

Step-by-step explanation:

Both the moon and earth are in the shape of spheres.

Surface area of a sphere of radius 'r' =4πr  

2

 

Let d  

1

​  

 be the diameter of the moon and d  

2

​  

 and be the diameter of the earth.

Let r  

1

​  

 be the radius of the moon and r  

2

​  

 be the radius of the earth.

Given d  

1

​  

=  

4

1

​  

d  

2

​  

 

=>2r  

1

​  

=  

4

1

​  

×2r  

2

​  

 

=>r  

1

​  

=  

4

1

​  

×r  

2

​  

 

Now, ratio of their surface areas is:

S  

1

​  

:S  

2

​  

 

=4πr  

1

​  

 

2

:4πr  

2

​  

 

2

 

=r  

1

​  

 

2

:r  

2

​  

 

2

 

=1  

2

:4  

2

 

=1:16

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