Final answer:
To find the mass of a marble cuboid, first convert the dimensions to centimeters and calculate the volume. Then multiply the volume by the density of marble (2.7g/cm³) to find the mass in grams, and convert it to kilograms. The result: the mass of the marble cuboid is 486kg.
Step-by-step explanation:
To calculate the mass of a cuboid made of marble, we need to use the formula for mass which is the product of its volume and its density. Since the density of marble is given in grams per cubic centimeter (g/cm³), and the dimensions of the cuboid are in meters, first we'll need to convert the dimensions of the cuboid to centimeters.
The dimensions of the cuboid are 1m x 0.6m x 0.3m. In centimeters, these dimensions are 100cm x 60cm x 30cm. The volume of the cuboid is found by multiplying the length by the width by the height: Volume = 100cm x 60cm x 30cm = 180,000cm³.
Now we can calculate the mass using the density of marble, which is 2.7g/cm³. The mass (m) is density (ρ) times volume (V), so:
m = ρV = 2.7g/cm³ x 180,000cm³ = 486,000g.
Since 1 kilogram is equal to 1000 grams, we convert the mass to kilograms:
Mass in kilograms = 486,000g ÷ 1000 = 486kg.
Therefore, the mass of the marble cuboid is 486 kilograms.