A 2.60 kg steel gas can holds 15.0 L of gasoline when full. What is the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
To find the average density of the full gas can, you need to consider the total mass and volume of both the steel can and the gasoline.
First, let's find the volume occupied by the steel can. The volume of a shape can be calculated using the formula Volume = length × width × height. However, we don't have the dimensions of the can, so we'll estimate its volume by assuming it is a rectangular prism.
Next, let's find the volume occupied by the gasoline. We are given that the can holds 15.0 L of gasoline, so the volume of the gasoline is 15.0 L.
Finally, to find the average density, divide the total mass of the gas can by its total volume. The total mass is the sum of the mass of the steel can and the mass of the gasoline.
Let's calculate it step by step:
Step 1: Estimate the volume of the steel can
- Since we don't have the dimensions of the can, let's assume it to be a rectangular prism.
- Estimate the length, width, and height of the can.
- For example, let's assume the length = 20 cm, width = 10 cm, and height = 15 cm.
- Calculate the volume of the steel can using the formula Volume = length × width × height.
- In this case, the volume of the steel can would be 20 cm × 10 cm × 15 cm = 3,000 cm³.
Step 2: Convert the volume of the steel can to liters
- Since the volume of gasoline is given in liters, we need to convert the volume of the steel can to liters.
- 1 cm³ is equal to 0.001 L, so the volume of the steel can in liters is 3,000 cm³ × 0.001 L/cm³ = 3 L.
Step 3: Calculate the total volume of the gas can
- The total volume is the sum of the volume of the steel can and the volume of the gasoline.
- In this case, the total volume would be 3 L + 15 L = 18 L.
Step 4: Calculate the total mass of the gas can
- We are given that the mass of the steel can is 2.60 kg.
- Assume that the density of the gasoline is approximately 0.75 kg/L.
- The mass of the gasoline can be calculated by multiplying its density by its volume: 0.75 kg/L × 15 L = 11.25 kg.
- Therefore, the total mass of the gas can is 2.60 kg + 11.25 kg = 13.85 kg.
Step 5: Calculate the average density of the gas can
- Divide the total mass of the gas can by its total volume.
- In this case, the average density would be 13.85 kg / 18 L = 0.77 kg/L (rounded to two decimal places).
Therefore, the average density of the full gas can, taking into account the volume occupied by both the steel and gasoline, is approximately 0.77 kg/L.