Question

You need to determine the mass of a sample of an element for a science project. The element is in the shape of a rectangular prism with a length of 6 millimeters, a width of 3 millimeters, and a height of 8 millimeters. The density of the element is 2.7 grams per cubic centimeter. Find the mass of the element.

Answer 1

The mass of the element shaped as a rectangular prism with given dimensions and a density of 2.7 g/cm³ is calculated to be 0.3888 grams after converting the dimensions into centimeters and using the mass-density-volume relationship.

Step-by-step explanation:

To calculate the mass of the element, we must first find the volume of the rectangular prism, which is given by multiplying its length, width, and height. Since the measurements given are in millimeters, we need to convert them to centimeters before using the density formula.

The volume of the rectangular prism (in cubic centimeters) is:

V = (length in cm) × (width in cm) × (height in cm)

V = (0.6 cm) × (0.3 cm) × (0.8 cm) = 0.144 cm³

Now, using the density formula:

Density (ρ) = Mass (m) / Volume (V)

From the problem, we know the density of the element is 2.7 g/cm³, so we can rearrange the formula to solve for mass:

m = ρ × V = 2.7 g/cm³ × 0.144 cm³

Thus, the mass of the element is:

m = 0.3888 grams

Answer 2

To find the mass of the element, you need to multiply the density of the element by its volume. In this case, the element is in the shape of a rectangular prism. After calculating the volume, you can plug in the values to find the mass. The mass of the element is 3.888 grams.

Step-by-step explanation:

To find the mass of the element, we can use the formula:

Mass = Density x Volume

In this case, the volume of the rectangular prism can be found by multiplying its length, width, and height:

Volume = Length x Width x Height

Plugging in the values from the question:

Volume = 6 mm x 3 mm x 8 mm

Next, we convert the volume to cubic centimeters:

Volume = (6 mm x 3 mm x 8 mm) / (10 mm/cm)

Now, we can calculate the mass:

Mass = Density x Volume

Mass = 2.7 g/cm³ x (6 mm x 3 mm x 8 mm) / (10 mm/cm)

Simplifying the equation:

Mass = 2.7 g/cm³ x 1.44 cm³

Mass = 3.888 g

The mass of the element is 3.888 grams.