Question

(i) If the ratio of the volumes of two solid spheres is 1:8, the ratio of their curved surface areas is
(a) 1:2 (b) 1:4 (c) 1:8 (d) 1:16​

Answer 1

Step-by-step explanation:

Answer

Correct option is

B

1:4

Volume of a sphere of radius 'r' =

3

4

πr

3

Let r

1

be the radius of the first sphere and r

2

and be the radius of the second sphere.

Given, ratio of their volumes is: V

1

:V

2

=1:8

3

4

πr

1

3

:

3

4

πr

3

2

h=1:8

r

1

3

:r

2

3

=1:8

=>r

1

:r

2

=1:2

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

2

Now, ratio of their surface areas is:

S

1

:S

2

=4πr

1

2

:4πr

2

2

h

=r

1

2

:r

2

2

=1

2

:2

2

=1:4