Question

the surface areas of two spheres are in the ratio 1 : 4, find the ratio of their volumes.​

Answer 1

Step-by-step explanation:

Consider r and R as the radii of two spheres

We know that

4πR

2

4πr

2

=

4

1

So we get

(

R

r

)

2

=(

2

1

)

2

It can be written as

R

r

=

2

1

Consider V

1

and V

2

as the volumes of the spheres So we get

V

2

V

1

=

4/3πR

3

4/3πr

3

We can write it as

(

R

r

)

3

=(

2

1

)

3

=

8

1

Therefore, the ratio of their volumes is 1:8.

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Answer 2

Answer:

Consider r and R as the radii of two spheres

We know that

4πR²/4πr² = 4/1

So we get

( R/r )² =( 2/1 )²

It can be written as

R/r = 2/1

Consider V1 and V2 as the volumes of the spheres So we get

V1 / VV =4/3πR³/4/3πr³

We can write it as

( r/R )³ =( 1/2 )³ = 1/8

Therefore, the ratio of their volumes is 1:8.