Final answer:
To determine the mass of the block, its volume must be calculated first (207.72 cm³) and then multiplied by its density (8.57 g/cm³), yielding a mass of approximately 1780.1284 grams.
Step-by-step explanation:
To find the mass of the block given its dimensions and density, we need to first calculate the volume of the block and then use the density to determine the mass.
The volume (V) of a rectangular block is calculated by multiplying its length (l), width (w), and height (h):
V = l × w × h
Substituting the given dimensions:
V = 6.50 cm × 4.50 cm × 7.12 cm = 207.72 cm³
Now, using the formula for density (ρ) which is mass (m) divided by volume (V), ρ = m/V, the mass can be found by rearranging the formula to m = ρ × V:
m = 8.57 g/cm³ × 207.72 cm³
m = 1780.1284 g
Therefore, the mass of the block is approximately 1780.1284 grams.