Question

The surface areas of two spheres are in the ratio 16:9. Then find ratio of their volumes.

​

Answer 1

Answer:

Suppose radii of the two spheres arer

1

andr

2

respectively

∴ Surface areas of the two spheres are 4πr

1

2

and 4πr

2

2

respectively

According to question

4πr

2

2

=9:16⇒r

1

2

:r

2

2

=9:16

r

2

2

r

1

2

=

16

9

⇒(

r

2

r

1

)

2

=(

4

3

)

2

⇒r

1

:r

2

=3:4⇒(

r

2

r

1

)

3

=(

4

3

)

3

⇒

r

2

3

r

1

3

=

64

27

⇒r

1

3

:r

2

3

=27:64

Therefore ratio of their volumes=

3

4

πr

1

3

:

3

4

πr

2

3

=r

1

3

:r

2

3

=27:64