Question

In an old trunk, you find a cube of metal that you think may be aluminum, silver, lead, cobalt or tin. In lab you find that it has a mass of 222 g and a length of 2.7 cm. What is the metal? The density of each metal is given below at room temperature. O Lead (11.3 g/cm) O Silver (10.5 g/cm) Cobalt (8.90 g/cm) O Tin (7.31g/cm) Aluminum (2.70 g/cm)

Answer 1

The density of the metal cube is calculated to be approximately 11.28 g/cm³, which closely matches the density of lead (11.3 g/cm³), suggesting that the cube is made of lead.

Step-by-step explanation:

To determine the type of metal a cube is made of, you need to calculate its density and compare it with the given densities of possible materials. The density is calculated by dividing the mass of the cube by its volume.

The mass of the metal cube is given as 222 g, and the length of each side is 2.7 cm. The volume V of a cube is found by cubing the length of one of its sides: V = 2.7 cm × 2.7 cm × 2.7 cm = 19.683 cm³. The density ρ is then found by dividing the mass m by the volume V: ρ = m/V = 222 g / 19.683 cm³ ≈ 11.28 g/cm³.

Comparing this calculated density with the given densities, the closest match is lead (11.3 g/cm³). Therefore, the metal cube is most likely made of lead.

Answer 2

The density of old trunk is
`11.3 g/cm^3` and it is equal to the density of metal lead.

Step-by-step explanation:

Mass of the trunk , m= 222 g

Length of the cubic trunk = 2.7 cm

Volume of the cube =
`a^3`

Density of the truck =
`(Mass)/(Volume)`

`D=(m)/(a^3)=(222 g)/((2.7 cm)^3)=11.2787 g/cm^3\approx 11.3 g/cm^3`

The density of old trunk is
`11.3 g/cm^3` and it is equal to the density of metal lead.