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Sergeu [11.5K]
3 years ago
9

g A cylindrical tank with radius 7 m is being filled with water at a rate of 6 mଷ/min. How fast is the height of the water incre

asing? (Recall: V = πrଶh)
Mathematics
1 answer:
RoseWind [281]3 years ago
8 0

Answer:

  6/(49π) ≈ 0.03898 m/min

Step-by-step explanation:

  V = πr²h . . . . formula for the volume of a cylinder

  dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

  dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

  dh/dt ≈ 0.03898 m/min

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