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AnilSinghBora
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The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases. Q.4

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How can i solve this tough question of class 9th ncert of Surface areas and Volumes of math of exercise 13.4     of question no.4 . Give me the best and simple way for solving this question.  The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

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  1. Let 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)

    = 4r12/4r22

    = (r1/r2)2

    = (7/14)2 = (1/2)2 = ¼

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

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