A circle is growing so that the radius is increasing at the rate of 5 cm/min. How fast is the area of the circle changing at the instant the radius is 20 cm? Include units in your answer.

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Answer 1 · 2018-01-27T11:25:27

#(dA)/(dt)=200pi" cm"^2"/min"#

if#" "r="the radius of the circle"#

we are given that

#color(red)((dr)/(dt)=5 " cm/min")#

if#" "A=" the area of the circle "#

we want #[(dA)/(dt)]_(r=20)#

#(dA)/(dt)=color(red)((dr)/(dt))xx color(blue)((dA)/(dr)#

now for acircle

#A=pir^2#

#=>(dA)/(dr)=2pir#

#:.color(blue)( [(dA)/(dr)]_(r=20)=2pixx20=40pi) #

#(dA)/(dt)= color(red)(5)xx color(blue)(40pi)=200pi" cm"^2"/min"#