Finding rate of change
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Finding rate of change
Last updated at May 6, 2021 by Teachoo
Example 3 A stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?Let r be the radius of circle & A be the Area of circle Given that When stone dropped into a lake wavers movie in circle at speed to 4 cm per sec. i.e. Radius of circle increasing at a rate of 4 cm / sec. i.e. π π/π π = 4 cm/sec We need to calculate how fast area increasing when waves is 10 cm i.e. we need to calculate π π¨/π π at r = 10 We know that Area of circle is Οr2 Now ππ΄/ππ‘ = (π(ππ2))/ππ‘ =π (π(π2))/ππ‘ = Ο [π(π2)/ππ‘ Γ ππ/ππ] = Ο [ππ2/ππ Γ ππ/ππ‘] = Ο [2π Γ π π/π π] = Ο [2π Γ π] = 8Οr When r = 10 β ππ΄/ππ‘β€|_(π =10) = 8Ο Γ 10 β ππ΄/ππ‘β€|_(π =10) =80π Since Area is in cm2 & time is in sec ππ΄/ππ‘ = 80π πππ/πππ Hence the area is increasing at the rate of 80 Ο cm2/sec,