A cylindrical bucket is being filled with paint at a rate of 4 cm³/min. How fast is the level rising when the bucket starts to overflow? The bucket has a height of 50 cm and a radius of 10 cm. A)0.013 cm/min B)0.315 cm/min C)0.164 cm/min D)0.617 cm/min E)0.768 cm/min

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Quizplus · Accepted Answer

The rate at which the level of paint rises in the bucket depends on the volume of the paint being poured in and the dimensions of the bucket. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height. The rate at which the bucket is being filled is 4 cm^3/min. To find the rate at which the level rises, we divide the rate of volume increase by the cross-sectional area of the bucket, which is πr^2. So, the rate of height increase is (4 cm^3/min) / (π(10 cm)^2) = 4 / (π*100) cm/min ≈ 0.013 cm/min.

A Cylindrical Bucket Is Being Filled with Paint at a Rate