Question 4
The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

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Solution

Radius $r_{1}$ of spherical balloon = 7 cm

Radius $r_{2}$ of spherical balloon, when air is pumped in to it = 14 cm

$R e q u i r e d r a t i o = \frac{I n i t i a l s u r f a c e a r e a}{S u r f a c e a r e a a f t e r p u m p i n g a i r i n t o t h e b a l l o o n} = \frac{4 π r_{1}^{2}}{4 π r_{2}^{2}} = {(\frac{r_{1}}{r_{2}})}^{2} = {(\frac{7}{14})}^{2} = \frac{1}{4}$

The required ratio is 1:4.

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Surface area of a sphere

Standard IX Mathematics

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Question 4 The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Radius r1 of spherical balloon = 7 cm Radius r2 of spherical balloon, when air is pumped in to it = 14 cm Required ratio=Initial surface areaSurface area after pumping air into the balloon=4πr214πr22=(r1r2)2=(714)2=14 The required ratio is 1:4.

Question 4
The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.