Question
CBSEENMA9003457

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. 

Solution

Case I. r = 7 cm
∴ Surface area = 4straight pir2
equals 4 cross times 22 over 7 cross times left parenthesis 7 right parenthesis squared equals 616 space cm squared

Case II. r = 14 cm
∴ Surface area = 4πr2
equals 4 cross times 22 over 7 cross times left parenthesis 14 right parenthesis squared
= 2464 cm2

∴ Ratio of surface areas of the balloon = 616 : 2464
equals 616 over 2464 equals 1 fourth equals 1 space colon space 4

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