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

Let r1 and r2 represent the radii of a sphere before and after air is pumped into it, respectively.

So, r₁ = 7 cm and r₂ = 14 cm.

We know that, the surface area of the sphere = 4πr²

Here, ratio = initial surface area / Surface area after pumping air into the balloon

= 4πr₁²/4πr₂² = (r₁/r₂)²

= (7/14)² = (1/2)² = 1/4

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