Subscribe to our Youtube Channel - https://you.tube/teachoo

Last updated at May 29, 2018 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. 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 with the radius when r is 10cm i.e. we need to find change of volume w.r.t radius when r = 10 i.e. we need to find ๐๐ฃ๏ทฎ๐๐๏ทฏ when r = 10 we know that volume of sphere = 4๏ทฎ3๏ทฏ ฯr3 v = 4๏ทฎ3๏ทฏ ฯr3 Differentiate w. r. t radius ๐๐ฃ๏ทฎ๐๐๏ทฏ = ๐ 4๏ทฎ3๏ทฏ ๐๐3๏ทฏ๏ทฎ๐๐๏ทฏ ๐๐ฃ๏ทฎ๐๐๏ทฏ = 4๏ทฎ3๏ทฏ ฯ ๐ ๐3๏ทฏ๏ทฎ๐๐๏ทฏ ๐๐ฃ๏ทฎ๐๐๏ทฏ = 4๏ทฎ3๏ทฏ ฯ 3 ๐๏ทฎ2๏ทฏ ๐๐ฃ๏ทฎ๐๐๏ทฏ = 4๐ ๐๏ทฎ2๏ทฏ When r = 10 ๐๐ฃ๏ทฎ๐๐๏ทฏ = 4 ร ฯ ร (10)2 ๐๐ฃ๏ทฎ๐๐๏ทฏ = 400 ฯ Since volume is in cm3 & Radius is in cm So, ๐๐ฃ๏ทฎ๐๐๏ทฏ = 400ฯ ๐๐๐๏ทฎ๐๐๏ทฏ Hence, volume is increasing at the rate of 400 ฯ cm3/cm when r = 10 cm

Chapter 6 Class 12 Application of Derivatives

Serial order wise

About the Author

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.