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Derivatives : Related Rates and Rates of Change

1.Water is poured into a conical funnel at a rate of 1 cm3/s. The radius of the top of the funnel is 10 cm and the height of the funnel is 20 cm. Find the rate at which the water level is rising when it is 5 cm from the top of the funnel.

I know that I am suppose to use the volume of the cone

V=1pi r2h

2.A light is on the ground, 15 m from a wall. A woman, 1.6 m tall, walks away from the light and towards the wall at o.5 m/s. Calculate the rate of the change of the length of her shadow on the wall when the woman is 10 m from the wall.

I know that I should find the rate at which the tip of her shadow is moving.

3.A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope at a constant height (1.5 m) and walks away from beneath the pulley at 1.6 m/s. How fast is the bucket rising when he is 9 m away from the path of the rising cement bucket?

See attached file for full problem description.


Solution Summary

Related rates are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.