A cylindrical tank measuring 6.00 feet in diameter and 17 feet, 6 inches, in length is filled with room temperature water. How many kilograms and pounds does the water weight? The density of room temperature water is 1.00 g/mL.
1000 kg/m^3
V = pi (d^2/4)h
d = 6 ft = 1.83 m
h = 17.5 ft = 5.33 m
so V = [pi(1.83^2)/4 ]5.33 m^3
mass= 1000 * V in kg
there are about 2.2 pounds/kg
To find the weight of the water in the cylindrical tank, we need to calculate the volume of the tank first and then multiply it by the density of water.
1. The diameter of the cylinder is given as 6.00 feet, so we can calculate the radius by dividing it by 2:
Radius = Diameter / 2 = 6.00 feet / 2 = 3.00 feet
2. The length of the cylinder is given as 17 feet, 6 inches. We need to convert the inches to feet so that the units match. Since there are 12 inches in a foot, we can convert 6 inches to feet by dividing by 12:
Length = 17 feet + 6 inches / 12 = 17 feet + 0.5 feet = 17.5 feet
3. Now we can calculate the volume of the cylinder using the formula for the volume of a cylinder:
Volume = π * (radius^2) * length
Substituting the calculated values:
Volume = π * (3.00 feet)^2 * 17.5 feet
= 3.14159 * 9.00 feet^2 * 17.5 feet
≈ 475.01 cubic feet
4. The density of water is given as 1.00 g/mL. Since the volume is in cubic feet, we need to convert it to milliliters (mL):
Volume = 475.01 cubic feet * (0.0283168466 m^3 / 1 cubic foot) * (1000 mL / 1 m^3)
≈ 13,430.89 mL
5. Finally, we can calculate the weight of the water by multiplying the volume by the density:
Weight = Volume * Density
= 13,430.89 mL * 1.00 g/mL
= 13,430.89 g
To convert the weight to kilograms and pounds, we need to use the appropriate conversion factors:
6. To convert grams to kilograms, divide by 1000:
Weight in kilograms = 13,430.89 g / 1000
≈ 13.43 kg
7. To convert grams to pounds, divide by 453.59237:
Weight in pounds = 13,430.89 g / 453.59237
≈ 29.58 pounds
Therefore, the water in the cylindrical tank weighs approximately 13.43 kilograms and 29.58 pounds.