Question

A hemispherical tank is filled with water and has a diameter of 11 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 is 21744 pounds

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 =
`(4)/(3)` πr³

∵ The tank is shaped a hemisphere

∵ The volume of a sphere = V =
`(4)/(3)` πr³

- Multiply it by one-half to find the volume of the hemisphere

∴ The volume of the tank =
`(1)/(2)` (
`(4)/(3)` πr³)

∴ The volume of the tank =
`(2)/(3)` πr³

∵ The hemisphere take has a diameter 11 feet

- The radius is one-half the diameter

∴ r =
`(1)/(2)` × 11 = 5.5 feet

- Substitute its value in the formula of the volume above

∵ The volume of the tank =
`(2)/(3)` 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