A hemisphere tank is filled with water and has a diameter of ten feet. If the water weighs 62.4 pounds per cubic foot, what is the total weight of water in a full tank?
(1/2)(4π/3 * (10/2)^3) ft^3 * 62.4 lb/ft^3 = 16340 lb
To find the total weight of water in a full hemisphere tank, we need to calculate the volume of the tank first and then multiply it by the weight of the water per cubic foot.
Step 1: Find the radius of the hemisphere tank
The diameter of the tank is given as 10 feet, so the radius (r) can be calculated by dividing the diameter by 2.
r = 10 ft / 2 = 5 ft
Step 2: Calculate the volume of the hemisphere tank
The volume of a hemisphere is given by the formula: V = (2/3) * π * r^3
Substituting the value of the radius:
V = (2/3) * π * (5 ft)^3 ≈ 523.6 ft^3
Step 3: Calculate the weight of water in the full tank
Given that the water weighs 62.4 pounds per cubic foot, we can multiply the volume of the tank by the weight of the water per cubic foot to find the total weight.
Total weight = Volume * Weight per cubic foot
Total weight = 523.6 ft^3 * 62.4 lb/ft^3 = 32,646.24 pounds
Therefore, the total weight of water in a full hemisphere tank is approximately 32,646.24 pounds.