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.