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Differentiation: Increase in height of sand pile with volume

At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately 3x the altitude. At what rate is the height of the pile changing when the pile is 15 feet high?

Solution Summary

Sand is poured through a conveyor belt on a conical pile at a constant rate. The rate of increase in height is calculated.

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Mukund Pandya, M.Sc.

Rating 5.0/5

Active since 2005

BSc, Vikram Uni. Ujjain
MSc, Vikram Uni. Ujjain
BEd, Bhopal University Bhopal
MA, Ravishankar University Raipur

Responses 965


Comments on Mukund's work:

"Sorry I attached the wrong figure for this question but seems your answer is still right. May I resend the problem with the correct figure and let you to double check with it? If I may, how to attach the correct figure?"

"Thank you Much appreciated"

"Thanks Mukund Very well presented"

"Great response with excellent explanation. Thank you."

"Detailed solution, with emphasis on the concept which makes me able to do other similar problems! Thank you"