Q20 of 79 Page 238

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

GIVEN : radius of balloon before the increase “r” = 7cm


radius of balloon after the increase “R” = 14cm


TO FIND : ratio of volumes of the balloon in both cases


PROCEDURE :


Volume of balloon before the increase “V1” = ×π ×r3


Volume of balloon after the increase “V2” = ×π ×R3


Ratio of the volumes in the 2 cases =


= = = = = =


∴ the ratio of volumes of the balloon in the two cases is = ie. 1 : 8.


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