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Last updated at Jan. 7, 2020 by Teachoo

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Ex 6.1, 12 The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing when the radius is 1 cm? Let r be the radius of air bubble Given ๐๐/๐๐ก = 1/2 cm/s The Bubble is a sphere Volume of bubble = Volume of sphere = 4/3 ๐๐^3 We need to find the rate at which volume of the bubble is increasing when radius is 1 cm โฆ(1) i.e. ๐๐ฃ/๐๐ก at r = 1 cm ๐๐ฃ/๐๐ก = ๐(4/3 ๐๐^3 )/๐๐ก = 4/3 ๐ (๐๐^3)/๐๐ก = 4/3 ๐ (๐๐^3)/๐๐ ๐๐/๐๐ก = 4๐/3 ใ3๐ใ^2 ๐๐/๐๐ก = 4๐๐^2 1/2 = 2๐๐^2 (From (1): ๐๐/๐๐ก=1/2) When radius is 1cm ๐๐ฃ/๐๐ก = 2๐(1)^2 ๐๐ฃ/๐๐ก = 2๐ Since volume is in cm3 & time is in sec So ๐๐ฃ/๐๐ก = ๐๐ cm3/sec Hence, volume is increasing at rate of 2๐ cm3/sec when radius = 1cm

Chapter 6 Class 12 Application of Derivatives

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.