the radius of a spherical balloon increases from 12cm to 16cm as air begin pumped into it.find the ratio of the surface area of the balloon in the two cases.
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Let surface area in first case and second case be S₁ and S₂ .
S₁ = 4 π r₁² ------------------( 1 )
S₂ = 4 π r₂² ---------------- ( 2 )
Dividing equation ( 1 ) by equation ( 2 )
=> S₁ / S₂ = 4 π r₁² / 4 π r₂²
=> S₁ / S₂ = r₁² / r₂²
= ( 12 )² / ( 16 )²
= 144 / 256
=> S₁ / S₂ = 9 / 16
=> S₁ : S₂ = 9 : 16
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