Last updated at April 19, 2021 by Teachoo

Transcript

Ex 6.1, 8 A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of balloon increases when radius is 15 cm.Since Balloon is spherical Let r be the radius of spherical balloon & V be the volume of spherical balloon. Given that The balloon is inflated by pumping in in 900 cubic cm of gas per sec i.e. Volume of balloon increasing at the rate of 900 cm3/sec i.e. ๐ ๐ฝ/๐ ๐ = 900 cm3/sec We need to calculate the rate of change at which radius of Balloon increases when radius is 15 cm i.e. we need to calculate ๐ ๐/๐ ๐ when r = 15 cm We know that Volume of sphere = V = 4/3 ฯr3 Now, ๐๐/๐๐ก = ๐(4/3 ๐๐3)/๐๐ก ๐๐/๐๐ก = 4/3 ฯ (๐ (๐3))/๐๐ก 900 = 4/3 ฯ (๐ (๐3))/๐๐ก 900 = 4/3 ฯ . (๐(๐3))/๐๐ก ร ๐ ๐/๐ ๐ 900 = 4/3 ฯ . (๐(๐3))/๐๐ ร ๐๐/๐๐ก 900 = 4/3 ฯ . 3r2 . ๐๐/๐๐ก 900 = 4 ร ฯ ร r2 . ๐๐/๐๐ก 900/(4 ร ๐ ร ๐2) = ๐๐/๐๐ก ๐ ๐/๐ ๐ = (๐๐๐ ร ๐)/(๐ ร ๐๐ ร ๐๐) We need to find ๐๐/๐๐ก at r = 15 cm ๐๐/๐๐ก = 900/(4 ร ๐ ร (15)^2 ) ๐ ๐/๐ ๐ = ๐/๐ Since radius in cm & time in sec ๐๐/๐๐ก = ๐/๐ cm/s Hence, the radius of the balloon is increasing at the rate of 1/๐ cm/sec when r = 15 cm.

Ex 6.1

Ex 6.1, 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.