The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

 Solution:

Let r1 and r2 be the radii of spherical balloon and spherical balloon when air is pumped into it respectively. So

r1 = 7cm

r2 = 14 cm

Now, Required ratio = (initial surface area)/(Surface area after pumping air into balloon)

= 4πr12/4πr22

= (r1/r2)2

= (7/14)2 = (1/2)2 = ¼

Therefore, the ratio between the surface areas is 1:4.