Respuesta :
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,
            [tex]V = \frac{2}{3} \pi r^{3}[/tex]...................................(2)
       From given, r = Radius of Hemisphere
            [tex]r = \frac{d}{2}[/tex]
              [tex]= \frac{4}{2}[/tex]
             r = 2 foot  Â
      From equation (2),    Â
              = [tex]\frac{2}{3}[/tex] × [tex]\pi[/tex] × [tex]2^{3}[/tex]
              = 16.755 cubic foot
Step:3
      From equation (1),
              = 16.775 × 62.4        (∵ Water weighs 62.4 pounds per cubic foot )
              = 1045.52 pounds     ( ∵ [tex]foot^{3}[/tex] × [tex]\frac{pounds}{foot^{3}}[/tex] = [tex]pounds[/tex] )
              ≅ 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.
