Last updated at April 19, 2021 by Teachoo

Transcript

Ex 6.1, 9 A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.Since Balloon is spherical Let r be the radius of balloon . & V be the volume of balloon. We need to find rate at which balloon volume is increasing when radius is 10cm i.e. We need to find change of volume w.r.t radius when r = 10 i.e. we need to find ๐ ๐ฝ/๐ ๐ when r = 10 cm We know that Volume of sphere = V = 4/3 ฯr3 Now, ๐๐/๐๐ = (๐ (4/3 ๐๐3))/๐๐ ๐๐/๐๐ = 4/3 ฯ ๐(๐3)/๐๐ ๐๐/๐๐ = 4/3 ฯ 3๐^2 ๐๐/๐๐ = 4๐๐^2 When r = 10 ๐๐/๐๐ = 4 ร ฯ ร (10)2 ๐๐/๐๐ = 400ฯ Since volume is in cm3 & Radius is in cm So, ๐๐/๐๐ = 400ฯ cm3/cm Hence, volume is increasing at the rate of 400 ฯ cm3/cm when r = 10 cm

Ex 6.1

Ex 6.1, 1
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Chapter 6 Class 12 Application of Derivatives (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.