The Radius Of A Right Circular Cone Is Increasing...

Anonymous

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The radius of a right circular cone is increasing at a rate of 4 inches per second and its height is decreasing at a rate of 5 inches per second. At what rate is the volume of the cone changing when the radius is 40 inches and the height is 40 inches in cubic inches per second?

 

Answer No.1

FabulousJay4

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We are given that: r'=4 (in inches per second) (radius is increasing) h'=-5 (inches persecond) (height isdecreasing) We want to find V' when r=40 and h=40. Since V=(1/3)bh=(1/3)(πr2)h then V'=(1/3)(πr2)'*h+(1/3)(πr2)*h'= =(1/3)(2πr*r')h+(1/3)(πr2)h'= =(1/3)(2π*402*4)*40+(1/3)(π*402)*(-5) =168000π (in cubic inches per second) (please verify the numerical calculations yourself) Do not forget to rate! Thanks

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