What is the mass in kilograms of an iceberg with a volume of 8975 ft^3?

What is the formula to calculate the mass of an iceberg based on its volume and density?

To calculate the mass of an iceberg, we can use the formula: \[ m = \rho V \] where: - \( m \) is the mass, - \( \rho \) is the density, and - \( V \) is the volume of the iceberg. First, we need to convert the volume given in cubic feet to cubic centimeters. Since the density of ice is given in g/cm^3, we need to convert the volume to the correct unit. We know that 1 foot is equal to 30.48 cm. Therefore, the volume of the iceberg in cubic centimeters is: \[ 8975 ft^3 \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) = 2.54 \times 10^8 cm^3 \] Now, we can calculate the mass of the iceberg by plugging in the values of density and volume into the formula: \[ \begin{gathered} m = 2.54 \times 10^8 \text{ cm}^3 \times 0.917 \\ m = 2.32 \times 10^8 \text{ g} \end{gathered} \] Therefore, the mass of the iceberg is 2.32x10^8 grams. To convert this to kilograms, we have: \[ 2.32 \times 10^5 \text{ kg} \] So, the mass of the iceberg in kilograms is 2.32x10^5 kg.

Calculating the Mass of an Iceberg

To calculate the mass of an iceberg based on its volume and density, we utilize the formula \( m = \rho V \), where \( m \) is the mass, \( \rho \) is the density, and \( V \) is the volume. In this case, the volume of the iceberg is given as 8975 ft^3. However, since the density of ice is provided in g/cm^3, we need to convert this volume from cubic feet to cubic centimeters. Given that 1 foot is equal to 30.48 cm, we can convert the volume as follows: \[ 8975 ft^3 \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) \left( \frac{30.48 \text{ cm}}{1 \text{ ft}} \right) = 2.54 \times 10^8 cm^3 \] Once we have the volume in the correct unit, we can calculate the mass by multiplying the volume by the density of ice (0.917 g/cm^3): \[ \begin{gathered} m = 2.54 \times 10^8 \text{ cm}^3 \times 0.917 \\ m = 2.32 \times 10^8 \text{ g} \end{gathered} \] Therefore, the mass of the iceberg is 2.32x10^8 grams. Converting this to kilograms, we get: \[ 2.32 \times 10^5 \text{ kg} \] So, the mass of the iceberg in kilograms is 2.32x10^5 kg. This calculation shows how the volume and density of an iceberg are used to determine its mass in a different unit.
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