Final answer:
The combined weight of the tank and water is 1605.75 lbs.
Step-by-step explanation:
The first step is to calculate the volume of the tank. The volume of a rectangular prism is found by multiplying the length, width, and height. In this case, the dimensions are 24 inches by 12 inches by 16 inches.
V = 24 in × 12 in × 16 in = 4608 in³
Next, we need to convert the volume from cubic inches to cubic feet. There are 12 inches in a foot, so we divide the volume by 12³ (12×12×12) to convert.
V = 4608 in³ ÷ 12³ in³/ft³ = 2 ft³
Now we can calculate the weight of the water. We are given that the tank is ¾ full, so we multiply the volume of the tank by ¾ to get the volume of the water.
V_water = 2 ft³ × ¾ = 1.5 ft³
To find the weight of the water, we multiply the volume by the unit weight of water:
Weight_water = V_water × 62.5 lbs/ft³ = 1.5 ft³ × 62.5 lbs/ft³ = 93.75 lbs
Next, we need to calculate the weight of the tank. The tank is made of 5 sheets of glass, each with a thickness of ½ inch. So the total thickness of the glass is 5 × ½ = 2.5 inches. The weight of the glass can be found by multiplying the volume by the unit weight of glass.
V_glass = (24 in × 12 in + 2×(24 in × 16 in + 12 in × 16 in)) × 2.5 in = 60480 in³
Weight_glass = V_glass × 162 lbs/ft³ = 60480 in³ × (1/12³) ft³/in³ × 162 lbs/ft³ = 1512 lbs
Finally, we can calculate the combined weight of the tank and water by adding the weight of the water to the weight of the glass:
Weight_combined = Weight_water + Weight_glass = 93.75 lbs + 1512 lbs = 1605.75 lbs