A rectangular glass container with internal base dimensions of 5\text{ cm} by 4\text{ cm} … — Armed Services Vocational Aptitude Battery (ASVAB)

A rectangular glass container with internal base dimensions of $5\text{ cm}$ by $4\text{ cm}$ contains water. A solid mineral specimen with a mass of $130\text{ g}$ is completely submerged into the water, causing the water level to rise by $2.5\text{ cm}$ without spilling. What is the density of the mineral specimen in $\text{g/cm}^3$ ?

Answer: 2.6 g/cm^3

Answer

The density of the mineral specimen is

2.6\text{ g/cm}^3

Density is calculated by dividing mass by volume (

\rho = \frac{m}{V}

). The water displacement method reveals the object's volume:

\text{Volume} = \text{length} \times \text{width} \times \Delta h = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

. Dividing the given mass of

130\text{ g}

by the displaced volume of

50\text{ cm}^3

yields exactly

2.6\text{ g/cm}^3

Step-by-Step Solution

Calculate the volume of the displaced water inside the rectangular container.

V = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

The volume of fluid pushed upward corresponds to the area of the base multiplied by the change in water height.

Equate the volume of the submerged solid to the displaced fluid volume.

V_{\text{specimen}} = 50\text{ cm}^3

By the principle of fluid displacement, a completely submerged solid displaces a volume of fluid exactly equal to its own physical volume.

Calculate the density of the specimen using the mass-to-volume ratio.

\rho = \frac{m}{V} = \frac{130\text{ g}}{50\text{ cm}^3} = 2.6\text{ g/cm}^3

Density is an intensive physical property defined as mass per unit volume.

Key Concept

Density is an intensive physical property of matter defined as mass per unit volume (

\rho = m/V

), determinable for irregular or submerged solids via fluid displacement.

Estimated Time:1m 30s

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