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a water tank is shaped like a hemishpere with a diamter of 10 feet. the tank is being filler at a rate of 34 gallons per minute. 1 cubic foot of water is about 7.5 gallons, how long will it take to completley fill the tank? Round to rhe nearest whole minute



Answer :

sqdancefan

Answer:

  58 minutes

Step-by-step explanation:

You want the time it takes to fill a 10 ft hemisphere at the rate of 34 gallons per minute, using 1 ft³ = 7.5 gallons.

Volume

The volume of a hemisphere is given by ...

  V = (1/2)(4/3)πr³ = 2/3πr³ . . . . . . where r = half the diameter

In cubic feet, the volume is ...

  V = 2/3π(5 ft)³ = 250π/3 ft³ ≈ 261.799 ft³

In gallons, that will be ...

  V = (261.799 ft³)×(7.5 gal/ft³) ≈ 1963.50 gal

Time

At the fill rate of 34 gallons/minute, the time required is ...

  (1963.50 gal)/(34 gal/min) ≈ 57.75 min

It will take about 58 minutes to fill the tank completely.

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