Final answer:
The total weight of water in a full hemispherical tank with a diameter of 22 feet is found by calculating the volume of the hemisphere and multiplying it by the weight of water per cubic foot (62.4 pounds). Using the formula for the volume of a hemisphere and the provided conversion factor, we can solve for the total weight to the nearest pound.
Step-by-step explanation:
The student asked for the total weight of water in a full hemispherical tank with a 22-foot diameter, given that water weighs 62.4 pounds per cubic foot. To solve this, we calculate the volume of the hemisphere using the formula for the volume of a sphere (which is (4/3)πr^3) and then divide it by 2 because we need the volume of just the hemisphere, not the whole sphere. The radius (r) will be half of the diameter, so 11 feet. The calculated volume in cubic feet, when multiplied by 62.4 pounds per cubic foot (the weight of water), gives us the total weight of the water in the tank.
The volume of the hemisphere is ½ * (4/3)πr^3 = ½ * (4/3)π*11^3. Then, we find the total weight by multiplying the volume by the density of water: Total weight = Volume * Density of water. This results in the correct weight to the nearest pound, which we match with the given options (A through D).
Using unit conversion factors is crucial in this problem to ensure that all units align to calculate the weight accurately. In this case, we are converting cubic feet of water to pounds of water, using the given factor that one cubic foot of water weighs 62.4 pounds.