Question

A block of lead has dimensions of 5.4 cm by 4.5 cm by 5.9 cm. The block weighs 1587 g. From this information, calculate the density.

a) m = 1587 g, V = 5.4 cm³, Density = 294.167 g/cm³
b) m = 1587 g, V = 5.4 cm³, Density = 294.167 kg/cm³
c) m = 1587 kg, V = 5.4 cm³, Density = 294.167 g/cm³
d) m = 1587 g, V = 1587 cm³, Density = 1 g/cm³

Answer 1

The correct density of the lead block is approximately 11.074 g/cm³, calculated by dividing the mass (1587 g) by the volume (143.37 cm³). None of the initial options are correct.

Step-by-step explanation:

To calculate the density of a lead block given its dimensions and weight, we must first find its volume and then use the mass to calculate density using the formula Density = Mass / Volume. The dimensions of the lead block are 5.4 cm x 4.5 cm x 5.9 cm, and it weighs 1587 g.

The volume (V) of the block is calculated by multiplying its length by its width and height:

V = 5.4 cm × 4.5 cm × 5.9 cm = 143.37 cm³

Now, using the mass (m = 1587 g), we can calculate the density (d) using the formula:

Density = m / V = 1587 g / 143.37 cm³ = 11.074 g/cm³ (rounded to three decimal places)

Therefore, none of the options (a, b, c, d) provided initially are correct. The correct density of the lead block is approximately 11.074 g/cm³.