anonymous
  • anonymous
Related Rates: I know I have to do derivatives but I'm stuck on how to get from being given dv/dt to finding area. Also confused about finding radius when not given dr/dt only the height A chemical tank is leaking a toxic substance at a rate of 100cm^3/minute. Slick is semi-circ. in shape and has a thicknesss of .5cm a) After 1 hour how big an area does the slick cover? b) At 1 hour, at what rate is the radius of the slick changing?
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
i think if we just half the height, we can create a full circle model
amistre64
  • amistre64
V = pir^2 h/2 V' = 2pi r r' h/2 + pi r h'/2 ; but h' = 0 since the height is not changing V' = pi r r' h 100 = .25 pi r r' 400/pi = r r' ------------------------------------ area covered is just the base of the circle regardless of height A = pi r^2 A' = 2pi r r' ... per minute, we already have determined the r r' = 400/pi A' = 2pi(400/pi) = 800 cm^2 per minute
amistre64
  • amistre64
use 60 minutes to determine the area after an hour use the Area at an hour to determine the radius, and solve for r' in the V' setup

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amistre64
  • amistre64
might have some errors in calculations ... but the concept should be sound
amistre64
  • amistre64
im thinking i mentally halved the height to begin with and it should be: 100 = .5 pi r r' 200/pi = r r'

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