Finding rate of change
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Finding rate of change
Last updated at April 14, 2021 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 = π & Area of circle = A We need to find rate of change of Area w. r. t Radius i.e. we need to calculate π π¨/π π We know that Area of Circle = A = γππγ^2 Finding π π¨/π π ππ΄/ππ = (π (γππγ^2 ))/ππ ππ΄/ππ = π (πγ(πγ^2))/ππ ππ΄/ππ = π(2π) π π¨/π π = ππ π When r = 3 cm ππ΄/ππ = 2Οr Putting r = 3 cm β ππ΄/ππβ€|_(π = 3)= 2Ο Γ 3 β ππ΄/ππβ€|_(π = 3) = 6Ο Since Area is in cm2 & radius is in cm ππ΄/ππ = 6Ο cm2/cm Hence, Area is increasing at the rate of 6Ο cm2/ cm when r = 3 cm (ii) When r = 4 cm ππ΄/ππ = 2Οr Putting r = 4 cm ππ΄/ππ = 2Ο Γ 4 ππ΄/ππ = 8Ο Since Area is in cm2 & radius is in cm π π¨/π π = 8Ο cm2/cm Hence, Area is increasing at the rate of 8Ο cm2/cm when r = 4 cm