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
From equation (2),
= [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.
