The density of titanium is 4.51 g>cm3. What is the volume (in cubic inches) of 2.54 lb of titanium?

검증된 단계별 안내

Convert the mass of titanium from pounds to grams using the conversion factor: 1 lb = 453.592 g.

Calculate the volume in cubic centimeters using the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \), where the mass is in grams and the density is 4.51 g/cm³.

Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 inch = 2.54 cm, so \( 1 \text{ cm}^3 = \left(\frac{1}{2.54}\right)^3 \text{ in}^3 \).

Multiply the volume in cubic centimeters by the conversion factor to get the volume in cubic inches.

Ensure all units are correctly converted and consistent throughout the calculation.

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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, typically expressed in grams per cubic centimeter (g/cm³) in the metric system. It is a crucial property that helps determine how much space a given mass of a substance occupies. In this question, the density of titanium allows us to relate its mass to its volume, which is essential for solving the problem.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this question, we need to convert the mass of titanium from pounds (lb) to grams (g) to use the given density. Understanding how to perform these conversions accurately is vital for ensuring that calculations yield correct results.

Volume Calculation

Volume calculation involves determining the space occupied by a substance, which can be derived from its mass and density using the formula: Volume = Mass / Density. In this context, once the mass of titanium is converted to grams, applying this formula will allow us to find the volume in cubic centimeters, which can then be converted to cubic inches for the final answer.