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Multiple Choice
Suppose a cubic box contains so much air at that the mass of the air inside is equal to the mass of of water. What would be the side length of such a box?
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Verified step by step guidance
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First, understand that the problem involves equating the mass of air inside a cubic box to the mass of 1.0 L of water. The density of water is 1 kg/L, so the mass of 1.0 L of water is 1 kg.
Next, recall that the density of air at 0°C is approximately 1.29 kg/m³. This means that for a given volume of air, the mass can be calculated using the formula: mass = density × volume.
Since the box is cubic, its volume can be expressed as V = s³, where s is the side length of the cube. We need to find the side length s such that the mass of the air inside the cube equals 1 kg.
Set up the equation for the mass of the air: 1.29 kg/m³ × s³ = 1 kg. This equation relates the density of air, the volume of the cube, and the mass of the air.
Solve for s by rearranging the equation: s³ = 1 kg / 1.29 kg/m³. Then, take the cube root of both sides to find the side length s.