To find the total weight of the water in a full hemispherical tank, we first need to calculate the volume of the tank and then use the weight density of water to find the total weight.
The formula for the volume V of a hemisphere is given by:
V = (2/3) * π * r³
where r is the radius of the hemisphere. The diameter of the tank is 20 feet, which means the radius is:
r = diameter / 2 = 20 feet / 2 = 10 feet
Now we can substitute the radius into the volume formula:
V = (2/3) * π * (10)³
This simplifies to:
V = (2/3) * π * 1000 = (2000/3) * π ≈ 2093.33 cubic feet
Next, we know the weight of water is 624 pounds per cubic foot. To find the total weight, we multiply the volume by the weight density:
Weight = Volume * Weight Density
Weight = 2093.33 cubic feet * 624 pounds/cubic foot ≈ 1,306,000 pounds
Rounding to the nearest pound gives us:
Total Weight ≈ 1306000 pounds
Therefore, the total weight of the water in the full tank is approximately 1,306,000 pounds.