Final answer:
To calculate the density of the metal cube, convert its side length from mm to cm, find the volume using the cube's volume formula (V = s³), and then divide the given mass by the calculated volume. The approximate density is 4.03 g/cm³, which does not exactly fit the provided answer choices, possibly due to a rounding discrepancy.
Step-by-step explanation:
The student's question involves calculating the density of a small cube of metal given its mass and side length.
Density is characterized by the ratio of an object's mass to its volume. The side of the cube is given as 18.2 mm, which we first convert to centimeters because density is typically expressed in g/cm³. Since 1 mm is equal to 0.1 cm, we have:
Side length = 18.2 mm = 1.82 cm
To find the volume of the cube, we raise this value to the power of three, since the volume of a cube is calculated by taking the length of one side and multiplying it by itself three times (V = s³). Therefore:
Volume = (1.82 cm) ³ = 6.0292 cm³
Now, to calculate the density, we divide the mass of the metal cube by its volume:
Density = Mass / Volume
Density = 24.3 g / 6.0292 cm³
Density ≈ 4.03 g/cm³
However, since this result does not appear in the choices, it's possible there is a rounding error, or that the given options contain a mistake. In a real-world situation, the student would be informed of the correct calculation process and also advised to check the answer options and consider significant figures or other possible rounding guidelines used in their classroom or text.