Question

A hemispherical tank is filled with water and has a diameter of 4 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

Answer 1

The total weight of the water in a full tank, to the nearest pound is 1056 pounds, if water filled with water in the 4 diameter hemispherical tank and weighs 62.4 pounds per cubic foot.

Step-by-step explanation:

         The given is,

              A hemispherical tank is filled with water and has a diameter of 4 feet.

              Water weighs 62.4 pounds per cubic foot

Step:1

             Formula to weight of water is,

                          = Volume of water tank × weight of water per foot......(1)

Step:2

             Formula to find volume of the tank is,

                        $V = \frac{2}{3} \pi r^{3}$...................................(2)

             From given, r = Radius of Hemisphere

                        $r = \frac{d}{2}$

                           $= \frac{4}{2}$

                         r = 2 foot    

            From equation (2),        

                            = $\frac{2}{3}$ × $\pi$ × $2^{3}$

                            = 16.755 cubic foot

Step:3

            From equation (1),

                            = 16.775 × 62.4              (∵ Water weighs 62.4 pounds per cubic foot )

                            = 1045.52 pounds        ( ∵ $foot^{3}$ × $\frac{pounds}{foot^{3}}$ = $pounds$ )

                            ≅ 1046 pounds

            Weight of water in tank = 1046 pounds

Result:

           The total weight of the water in a full tank, to the nearest pound is 1056 pounds, if a hemispherical tank is filled with water and it has 4 feet diameter and water weighs 62.4 pounds per cubic foot.