The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of their surface areas.

1:5

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1:7

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1:9

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1:4

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Solution

The correct option is D
1:4

Initial radius of spherical balloon, $r_{1} = 7 cm$

Final radius (radius of spherical balloon after air is pumped into it), $r_{2} = 14 cm$

$R e q u i r e d r a t i o = \frac{i n i t i a l s u r f a c e a r e a}{F i n a l s u r f a c e a r e a} = \frac{4 π r_{1}^{2}}{4 π r_{2}^{2}} = (\frac{r_{1}}{r_{2}})^{2} = (\frac{7}{14})^{2} = \frac{1}{4}$

Hence, the required ratio is 1:4.

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The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of their surface areas.

The correct option is D 1:4 Initial radius of spherical balloon, r1=7 cm Final radius (radius of spherical balloon after air is pumped into it), r2=14 cm Required ratio=initial surface areaFinal surface area =4πr214πr22 =(r1r2)2 =(714)2 =14 Hence, the required ratio is 1:4.