Question

The diameter of the moon is approximately one fourth of the diameter of

the earth. Find the ratio of their surface areas.
​

Answer 1

Answer:

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

Answer 2

Answer:

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