Answer:
The total weight of the water in a full tank is 21744 pounds
Step-by-step explanation:
To solve the problem find the volume of the tank and multiply it by water weighs pounds per cubic foot to find the total weight of the water in a full tank
The formula of the volume of a sphere is V = [tex]\frac{4}{3}[/tex] πr³
∵ The tank is shaped a hemisphere
∵ The volume of a sphere = V = [tex]\frac{4}{3}[/tex] πr³
- Multiply it by one-half to find the volume of the hemisphere
∴ The volume of the tank = [tex]\frac{1}{2}[/tex] ( [tex]\frac{4}{3}[/tex] πr³)
∴ The volume of the tank = [tex]\frac{2}{3}[/tex] πr³
∵ The hemisphere take has a diameter 11 feet
- The radius is one-half the diameter
∴ r = [tex]\frac{1}{2}[/tex] × 11 = 5.5 feet
- Substitute its value in the formula of the volume above
∵ The volume of the tank = [tex]\frac{2}{3}[/tex] π(5.5)³
∴ The volume of the tank = 348.4549852 feet³
Now lets find the total weight
∵ The water weighs 62.4 pounds per cubic foot
- Multiply the volume by 62.4
∴ The total weight of the water = 62.4 × 348.4549852
∴ The total weight of the water = 21743.59107
- Round it to the nearest pound (whole number)
∴ The total weight of the water = 21744 pounds
The total weight of the water in a full tank is 21744 pounds
