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Finding rate of change
Ex 6.1, 1 You are here
Ex 6.1,17 (MCQ)
Example 5
Ex 6.1,15 Important
Example 6
Ex 6.1,16
Ex 6.1, 18 (MCQ) Important
Example 2
Ex 6.1,2
Example 35
Example 3
Ex 6.1,5 Important
Ex 6.1,3
Ex 6.1,6
Ex 6.1,12
Ex 6.1,13 Important
Misc 16 (MCQ)
Ex 6.1,14
Example 31 Important
Ex 6.1,4 Important
Example 30 Important
Example 4 Important
Ex 6.1,7
Ex 6.1,8
Ex 6.1,9
Ex 6.1,11 Important
Misc 2 Important
Ex 6.1,10 Important
Example 32 Important
Finding rate of change
Last updated at May 29, 2023 by Teachoo
Ex 6.1, 1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cmLet Radius of circle = ๐ & Area of circle = A We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐ ๐จ/๐ ๐ We know that Area of Circle = A = ใ๐๐ใ^2 Finding ๐ ๐จ/๐ ๐ ๐๐ด/๐๐ = (๐ (ใ๐๐ใ^2 ))/๐๐ ๐๐ด/๐๐ = ๐ (๐ใ(๐ใ^2))/๐๐ ๐๐ด/๐๐ = ๐(2๐) ๐ ๐จ/๐ ๐ = ๐๐ ๐ When r = 3 cm ๐๐ด/๐๐ = 2ฯr Putting r = 3 cm โ ๐๐ด/๐๐โค|_(๐ = 3)= 2ฯ ร 3 โ ๐๐ด/๐๐โค|_(๐ = 3) = 6ฯ Since Area is in cm2 & radius is in cm ๐๐ด/๐๐ = 6ฯ cm2/cm Hence, Area is increasing at the rate of 6ฯ cm2/ cm when r = 3 cm (ii) When r = 4 cm ๐๐ด/๐๐ = 2ฯr Putting r = 4 cm ๐๐ด/๐๐ = 2ฯ ร 4 ๐๐ด/๐๐ = 8ฯ Since Area is in cm2 & radius is in cm ๐ ๐จ/๐ ๐ = 8ฯ cm2/cm Hence, Area is increasing at the rate of 8ฯ cm2/cm when r = 4 cm