Answer: The volume of hope diamond is \(2.53cm^3\)
Explanation:
We are given:
Mass of hope diamond = 44.4 carat
To convert this into milligrams, we use the conversion factor:
1 carat = 200 mg
So, \(44.4carat\times (\frac{200mg}{1carat})=8880mg\)
To calculate mass of a substance, we use the equation:
\(\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}\)
We are given:
Density of hope diamond = \(3.51g/cm^3\)
Mass of hope diamond = 8880 mg = 8.88 g (Conversion factor: 1 g = 1000 mg)
Putting values in above equation, we get:
\(3.51g/cm^3=\frac{8.88g}{\text{Volume of hope diamond}}\\\\\text{Volume of hope diamond}=2.53cm^3\)
Hence, the volume of hope diamond is \(2.53cm^3\)
