Water is being poured at a rate of 15 cubic feet per minute into a conical reservoir that t is 20 feet deep and has a top radius of 10 feet. How long will it take to fill the empty reservoir?

Question

I know how to find the rate of the water rising when the height of the water is 4 feet or 16 feet but I can't figure out what to do when the height is equal to zero. Any advice would be nice, thanks in advance!

Answer 1

When the tank reaches full capacity what will the volume be? Whatever that volume, how may 15 ft³ will it contain? It takes one minute for each 15 ft³ to enter the tank, so whatever your answer is to the 2nd question above will be the number of minutes to fill the tank. No calculus is required to answer this question.

Use 1/3 π r²h to answer the first question. Divide by 15 ft³ to answer the 2nd question.