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.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

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.

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE