Question

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

Answer 1

Answer:

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We assume that r1 and r2 be the radii of spherical balloon and spherical balloon when air is pumped into it respectively. So,

r1 = 7cm

r2 = 14 cm

Now, Required ratio = (initial surface area)/(Surface area after pumping air into balloon)

= 4(r1)²/4(r2)²

= (r1/r2)²

= (7/14)² = (1/2)² = ¼

Therefore, the ratio between the surface areas is 1:4.

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Answer 2

QuestioN :

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

GiveN :

• Radius of balloon = r =  7 cm  

• Radius of pumped balloon = R = 14 cm

To FiNd :

• The ratio of surface areas of the balloon in the two cases.

ANswer :

The ratio of surface areas of the balloon in the two cases is 1 : 4.

SolutioN :

Ratio of surface area = (TSA of balloon with r = 7 cm)/(TSA of balloon with R = 14 cm)

= (4πr²)/(4πR²)

= r²/R²

= (7)²/(14)²

= 49/196

= 1/4

∴Hence,  the ratio of surface areas of the balloon in the two cases is 1 : 4.

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