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Ex 13.4, 4 - The radius of a spherical balloon increases - Area Of Sphere

  1. Chapter 13 Class 9 Surface Areas and Volumes
  2. Serial order wise
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Ex 13.4 , 4 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. Let r1 be the radius of smaller balloon = 7 cm and r2 be the radius of larger balloon = 14 cm Surface Area of sphere = 4๐œ‹r2 โˆด Ratio of their surface areas = (๐‘†๐‘ข๐‘Ÿ๐‘“๐‘Ž๐‘๐‘’ ๐‘Ž๐‘Ÿ๐‘’๐‘Ž ๐‘œ๐‘“ ๐‘ ๐‘š๐‘Ž๐‘™๐‘™๐‘’๐‘Ÿ ๐‘๐‘Ž๐‘™๐‘™๐‘œ๐‘›)/(๐‘†๐‘ข๐‘Ÿ๐‘“๐‘Ž๐‘๐‘’ ๐ด๐‘Ÿ๐‘’๐‘Ž ๐‘œ๐‘“ ๐‘๐‘–๐‘”๐‘”๐‘’๐‘Ÿ ๐‘๐‘Ž๐‘™๐‘™๐‘œ๐‘›) = 4๐œ‹๐‘Ÿ12/4๐œ‹๐‘Ÿ22 = ๐‘Ÿ12/๐‘Ÿ22 = 7^2/ใ€–14ใ€—^2 = (7 ร— 7)/(14 ร— 14) = 1/4 Thus , the required ratio of their surface areas = 1 : 4

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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