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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 surface areas of the balloon in the two cases. - Mathematics

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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 surface areas of the balloon in the two cases.

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Solution

Radius (r1) of spherical balloon = 7 cm

Radius (r2) of spherical balloon, when air is pumped into it = 14 cm

`"Required ratio "="Initial surface area"/"Surface area after pumping air into balloon"`

                         `= (4pir_1^2)/(4pir_2^2) = (r_1/r_2)^2`

                         `= (7/14)^2 = 1/4`

Therefore, the ratio between the surface areas in these two cases is 1:4.

Concept: Surface Area of a Sphere
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APPEARS IN

NCERT Class 9 Maths
Chapter 13 Surface Area and Volumes
Exercise 13.4 | Q 4 | Page 225

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