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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
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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
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GiveN:-
To FinD :-
AnsweR :-
Here we are considering the balloon as a sphere . And we know , the Curves Surface area of a sphere as ,
[tex]\large\boxed{\boxed{\red{\sf CSA_{sphere}\:=\:4\pi r^2 }}}[/tex]
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 .
[tex]\Large{\boxed{\pink{\sf Required\:Ratio = 4 :25 }}}[/tex]