(a) Three spheres of equal size are composed of aluminum (density = 2.70 g/cm³), silver (density = 10.49 g/cm³), and nickel (density = 8.90 g/cm³). List the spheres from lightest to heaviest.

검증된 단계별 안내

Identify the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \).

Since the spheres are of equal size, they have the same volume.

To compare the masses, rearrange the density formula to \( \text{Mass} = \text{Density} \times \text{Volume} \).

Calculate the mass for each sphere using their respective densities and the same volume.

List the spheres in order of increasing mass based on their calculated masses: Aluminum, Nickel, Silver.

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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). It is a crucial property that helps determine how heavy an object is for a given size. In this question, the densities of aluminum, silver, and nickel are provided, allowing for a comparison of their weights based on equal volumes.

Mass and Volume Relationship

The relationship between mass and volume is fundamental in understanding how density affects the weight of objects. For spheres of equal size, the mass of each sphere can be calculated by multiplying its density by its volume. This relationship allows us to rank the spheres based on their densities, as higher density indicates greater mass for the same volume.

Comparative Analysis

Comparative analysis involves evaluating different items based on specific criteria—in this case, the densities of the metals. By comparing the densities of aluminum, silver, and nickel, we can determine their relative weights when the spheres are of equal size. This analysis is essential for accurately listing the spheres from lightest to heaviest.

(a) Three spheres of equal size are composed of aluminum (density = 2.70 g/cm3), silver (density = 10.49 g/cm3), and nickel (density = 8.90 g/cm3). List the spheres from lightest to heaviest.