The 75 g piece of lead has a larger volume (approximately 6.61 cm³) compared to the 25 g piece (approximately 2.20 cm³), but both pieces have the same density since density is an intensive property of a substance, which remains constant irrespective of the amount.
To compare the volumes and densities of two pieces of lead with different masses, we can apply the formula that density is equal to mass divided by volume. Given that both samples are lead, we can assume they have the same density. Thus, volume can be found by dividing the mass by the density of lead. The question does not provide the density of lead directly, but we can infer it from the example given where a cube of lead with 90.7 g has an edge length of 2.00 cm. Calculating this (2 cm × 2 cm × 2 cm = 8 cm³) and dividing 90.7 g by 8 cm³ gives us a density of about 11.34 g/cm³ for lead.
Applying the formula to our two masses of lead:
- For the 25 g piece, volume = mass / density = 25 g / 11.34 g/cm³ ≈ 2.20 cm³
- For the 75 g piece, volume = mass / density = 75 g / 11.34 g/cm³, ≈ 6.61 cm³
The densities for both pieces remain constant at 11.34 g/cm³ because density is an intensive property which does not change with the size of the sample.
Although the 75 g piece of lead has a larger volume than the 25 g piece due to its greater mass, both pieces have the same density.