SOLUTION: .An inverted square pyramid has a height equal to 8m and a top edge equal to 3m. Initially, it contains water to a depth of 5m. a. what is the initial volume of the water in

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Question 1170533: .An inverted square pyramid has a height equal to 8m and a top edge equal to 3m. Initially, it contains water to a depth of 5m.
a. what is the initial volume of the water in the tank?
b. If additional water is to be pumped into the tank at the rate of 20gallons per minute, how many hours will it take to fill the tank?
Answer by ikleyn(52787) About Me  (Show Source):
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An inverted square pyramid has a height equal to 8m and a top edge equal to 3m. Initially, it contains water to a depth of 5m.
a. what is the initial volume of the water in the tank?
b. If additional water is to be pumped into the tank at the rate of 20 gallons per minute, how many hours will it take to fill the tank?
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The full volume of the pyramid is  V = %281%2F3%29%2Aa%5E2%2Ah = %281%2F3%29%2A3%5E2%2A8 = 3*8= 24 m^3.


The volume occupied by water is  %285%2F8%29%5E3%2AV = %285%2F8%29%5E3%2A24 = 5.589 m^3.        ANSWER to question (a)


The empty volume to be filled by water is  24 - 5.589 = 18.411 m^3



The rate of filling 20 gallons per minute = 20*0.003785 = 0.0757 m^3/minute.



The time to fill the empty volume is 


    18.411%2F0.0757 minutes = 143.21 minutes = 2 hours and 23.21 minutes (about two and half hours).    ANSWER to question (b)

Solved.