Question

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if radius of balloon increases from 14 cm to 35 cm as air is being pumped into it.find ratio of their surface area​

Answer 1

GiveN:-

• The radius of balloon increases from 14cm to 35 cm .

To FinD :-

• The ratio of their surface areas .

AnsweR :-

Here we are considering the balloon as a sphere . And we know , the Curves Surface area of a sphere as ,

$\large\boxed{\boxed{\red{\sf CSA_{sphere}\:=\:4\pi r^2 }}}$

CSA of initial sphere :-

⇒ CSA = 4 π r²

⇒ CSA = 4 π ( 14cm)²

⇒ CSA = 4π* (14cm)²

CSA of new sphere :-

⇒ CSA ' = 4 π r²

⇒ CSA' = 4 π (35cm)²

⇒ CSA' = 4π*(35 cm)²

Hence required Ratio :-

⇒ CSA : CSA' = 4π ( 14cm)² : 4π (35cm)²

⇒ CSA : CSA' = 14cm * 14cm / 35cm * 35cm

⇒ CSA : CSA' = 2 × 2 / 5 × 5

⇒ CSA : CSA' = 4 :25.

Hence the required Ratio is 4:25 .

$\Large{\boxed{\pink{\sf Required\:Ratio = 4 :25 }}}$