Anonymous From: - Posts: - Votes: - |
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? |

FabulousJay4 From: US Posts: 18 Votes: 54 |
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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