A rectangular solid measures 10.0 cm by 4.1 cm by 2.0 cm. The mass of this solid is 98.4 g. Calculate the density of the solid in g/mL.

Question

BlackTom AI · Accepted Answer

To tackle the problem, I start by identifying the given measurements and the formula needed.
The density is defined as density = mass / volume.
Next, I compute the volume of the rectangular solid using its dimensions: Volume = length × width × height = 10.0 cm × 4.1 cm × 2.0 cm = 82.0 cm^3.
With mass = 98.4 g, I substitute into the density formula: Density = 98.4 g / 82.0 cm^3 = 1.2 g/cm^3. Since 1 cm^3 equals 1 mL, the density in g/mL is 1.2 g/mL.
Now I evaluate each option one by one.
Option 0: 0.833 g/mL. This would require a mass of about 0.833 g/mL × 82 mL ≈ 68.3 g, which does not match the given mass of 98.4 g. Therefore this is incorrect.
Option 1: 1.2 g/mL. The calculation above yields exactly 1.2 g/mL, so this matches the correct result of mass/volume. This option is consistent with the computed values.
Option 2: this problem can not be solved. In this scenario, all necessary measurements (dimensions and mass) are provided, and a volume can be computed, so this claim is false.
Option 3: 82 g/mL. This would imply a density far larger than the mass divided by volume suggests, and confusing volume with density (or mixing units) leads to this incorrect figure. Thus this choice is not correct.
In summary, the correct approach uses Volume = 82.0 cm^3 and Density = 98.4 g / 82.0 cm^3 = 1.2 g/mL, while the other options arise from either miscalculations or misunderstandings of mass-volume relationships.

A rectangular solid measures 10.0 cm by 4.1 cm by 2.0 cm. The mass of this solid is 98.4 g. Calculate the density of the solid in g/mL. 单项选择题

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