Diamonds are measured in carats, and 1 carat=0.200g. The density of diamonds is 3.51g/cm3. what is the volume of a 5.0-carat diamond, expressed in liters?
mass = volume x density
mass = 5 carats x 0.200 g/carat = ?
density is given. Substitute and solve for volume in cc. Convert to L.
Post your work if you get stuck.
Please show the steps
To find the volume of a 5.0-carat diamond in liters, we need to first calculate the mass of the diamond and then use the density to find the volume.
Given:
1 carat = 0.200g
Density of diamonds = 3.51g/cm³
Step 1: Calculate the mass of the diamond in grams.
Mass = Carats * Conversion Factor
Mass = 5.0 carats * 0.200g/carat
Mass = 1.00g
Step 2: Calculate the volume of the diamond in cubic centimeters (cm³).
Density = Mass / Volume
Volume = Mass / Density
Volume = 1.00g / 3.51g/cm³
Volume ≈ 0.2845 cm³
Step 3: Convert the volume to liters.
1 liter = 1000 cm³
Volume (liters) = Volume (cm³) / 1000
Volume (liters) ≈ 0.2845 cm³ / 1000
Volume (liters) ≈ 0.0002845 liters
Therefore, the volume of a 5.0-carat diamond is approximately 0.0002845 liters.
To find the volume of a diamond, we first need to calculate the mass of the diamond using its carat weight, and then use the density to find the volume. Here's how you can do that:
Step 1: Calculate the mass of the diamond.
Given that 1 carat = 0.200g, for a 5.0-carat diamond, we can calculate the mass by multiplying the carat weight by the conversion factor:
Mass of diamond = 5.0 carats × 0.200 g/carat = 1.0 g
Step 2: Use the density to find the volume.
Given that the density of diamonds is 3.51 g/cm³, we can find the volume by dividing the mass by the density:
Volume of diamond = Mass of diamond / Density = 1.0 g / 3.51 g/cm³ ≈ 0.285 cm³
Step 3: Convert the volume to liters.
To convert the volume from cubic centimeters (cm³) to liters (L), we need to divide the volume by 1000:
Volume of diamond in liters = Volume of diamond / 1000 = 0.285 cm³ / 1000 ≈ 0.000285 L
Therefore, the volume of a 5.0-carat diamond is approximately 0.000285 liters.