Question

Iron has a density of 7.9 g/cm3. What is the mass of a cube of iron with the length of one side equal to 55.0 mm? Volume of a cube is calculated as V=s3 where s is the length of each side.

A) 2.1 × 10⁴ g
B) 4.3 × 10² g
C) 1.3 × 10³ g
D) 1.4 g
E) 2.3 × 10⁻² g

Answer 1

1.3 × 10³ g

Step-by-step explanation:

The mass of the cube can be found by using the formula:

mass = density x volume

From the question:

density = 7.9 g/cm³

length of one side (s) = 55 mm

First the length has to be converted to cm first before using it to find the volume.

`if \: 10mm = 1 \: cm \\ then \: 55mm = (55)/(10) * 1 \: cm \\ = 5.5cm`

Volume(v) of the cube = s³

`\therefore \: v = {5.5}^(3) = 166.375 \: {cm}^(3) \\ \\ \\ \therefore \: mass = 7.9 * 166.375 \\ = 1314.4 \approx \: 1.3 * {10}^(3) \: g`

Answer 2

To find the mass of the iron cube with a side length of 55.0 mm, convert the measurements to cm, calculate the volume, then apply the density of iron, 7.9 g/cm³, to find the mass, which is 1.3 × 10³ g. Option C is correct.

Step-by-step explanation:

The question is asking to determine the mass of a cube of iron when given the density of iron and the dimensions of the cube. To do this, first, we need to compute the volume of the cube. As we know, volume of a cube is calculated using the formula V = s³, where s is the length of a side of the cube. In this case, we have s = 55.0 mm, which we need to convert to centimeters to be compatible with the density unit. Since 1 mm = 0.1 cm, the side length in centimeters is 5.5 cm.

Calculating the volume we have:

V = 5.5 cm · 5.5 cm · 5.5 cm = 166.375 cm³.

Now, using the density of iron, Iron has a density of 7.9 g/cm³, we can find the mass of the iron cube by multiplying the volume by the density:

Mass = Density · Volume = 7.9 g/cm³ · 166.375 cm³ = 1314.3375 g, which we round to 1.3 × 10³ g in scientific notation. Therefore, the correct answer is C) 1.3 × 10³ g.