Water is flowing into a barrel in the shape of a right circular cylinder at the rate of 200 in³ per minute. If the radius of the barrel is 2 in, at what rate is the depth of the water changing when the water is 29 in deep? Round your answer to two decimal places. A) 50.00 in per minute B) 63.66 in per minute C) 20.26 in per minute D) 31.83 in per minute E) 15.92 in per minute

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Quizplus · Accepted Answer

The volume of a cylinder is V = πr²h. Given dV/dt = 200 in³/min and r = 2 in, we find dh/dt using the formula dV/dt = πr²(dh/dt). Solving for dh/dt gives dh/dt = (dV/dt) / (πr²) = 200 / (π(2)²) = 200 / (4π) ≈ 15.92 in/min.

Water Is Flowing into a Barrel in the Shape of a Right