An iceberg has a volume of 7655 ft2. What is the mass of the ice (in kg) composing the iceberg (at 0 °C)?

검증된 단계별 안내

Identify the density of ice at 0 °C, which is approximately 0.917 g/cm³.

Convert the volume of the iceberg from cubic feet to cubic centimeters. Use the conversion factor: 1 ft³ = 28316.8 cm³.

Calculate the mass of the ice by multiplying the volume in cm³ by the density of ice in g/cm³.

Convert the mass from grams to kilograms by dividing by 1000, since 1 kg = 1000 g.

Ensure all units are consistent and check calculations for accuracy.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Density

Density is defined as mass per unit volume and is a crucial property of materials. For ice, the density at 0 °C is approximately 0.917 g/cm³. This means that for every cubic centimeter of ice, it has a mass of 0.917 grams. Understanding density allows us to convert the volume of the iceberg into mass using the formula: mass = density × volume.

Volume Conversion

In this problem, the volume of the iceberg is given in square feet (ft²), which is a measure of area, not volume. To find the mass of the ice, we need to ensure that the volume is expressed in cubic feet (ft³). This requires understanding the dimensions of the iceberg and converting the area into a three-dimensional volume, which is essential for accurate calculations.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this case, we need to convert the mass from grams to kilograms, as the final answer requires the mass in kg. Knowing that 1 kg equals 1000 grams is essential for this conversion, ensuring that the final result is in the correct units.