What is the mass (in kilograms) of a cube of silver that measures 0.68m on each side, when the density of the sample is 10.5g/cm3
0.68m = 68 cm
68^3 = 3.14E5 = volume
mass = volume x density
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To find the mass of the cube, we need to use the formula:
mass = volume × density
First, we need to find the volume of the cube. Since the cube has sides measuring 0.68m, the volume can be calculated by taking the cube of the side length:
volume = (side length)³
volume = 0.68m × 0.68m × 0.68m
volume = 0.314m³
Now, we can calculate the mass by multiplying the volume by the density:
mass = volume × density
mass = 0.314m³ × 10.5g/cm³
However, we need to convert the density from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³) since the volume is in cubic meters:
density (kg/m³) = density (g/cm³) × 1000
density (kg/m³) = 10.5g/cm³ × 1000
density (kg/m³) = 10500 kg/m³
Now, we can calculate the mass:
mass = 0.314m³ × 10500 kg/m³
Calculating this, we find:
mass ≈ 3297 kg
Therefore, the mass of the silver cube is approximately 3297 kilograms.
To find the mass of the silver cube, we can use the formula:
Mass = Volume × Density
First, let's calculate the volume of the cube. The volume of a cube is given by the formula:
Volume = Side length × Side length × Side length
Given that the side length of the cube is 0.68m, we can substitute this value into the formula:
Volume = 0.68m × 0.68m × 0.68m
Now we need to convert the volume from cubic meters to cubic centimeters since the density is given in grams per cubic centimeter. There are 100 cm in a meter, so 1 cubic meter is equal to (100 cm) × (100 cm) × (100 cm) = 1,000,000 cubic centimeters.
Volume = (0.68m × 0.68m × 0.68m) × (1,000,000 cm3 / 1 m3)
Next, we can substitute the given density into the formula to find the mass:
Mass = Volume × Density
Finally, let's calculate the mass:
Mass = [(0.68m × 0.68m × 0.68m) × (1,000,000 cm3 / 1 m3)] × (10.5g/cm3)
After performing the calculation, the mass of the silver cube is obtained in grams. To convert it to kilograms, divide the value by 1000:
Mass (in kilograms) = Mass (in grams) / 1000
By following these calculations, you will find the mass (in kilograms) of the silver cube.