Question

Calculate the density in grams per cm^3 of a rectangular solid that is 4.30 cm by 2.41 cm by 0.556 meters and has a mass of 1050.0 grams.

a) 2.4 g/cm^3
b) 1.8 g/cm^3
c) 3.0 g/cm^3
d) 2.1 g/cm^3

Answer 1

b) 1.8 g/cm³

Step-by-step explanation:

density = mass/volume

convert 0.556 m to cm: 0.556 m x 100 cm/m = 55.6 cm

Volume = 4.30 x 2.41 x 55.6 = 576.183 cm³

m = 1050.0 g

Density = 1050.0 g / 576.183 cm³ = 1.822 g/cm³ ≈ 1.8 g/cm³

Answer 2

The density of the rectangular solid is calculated by first converting all dimensions into centimeters, computing the volume, and then dividing the mass by the volume. The final calculated density, considering significant figures, is 1.8 g/cm³.

Step-by-step explanation:

The density of a substance is defined as the mass per unit volume. To calculate the density, we need to first calculate the volume of the rectangular solid. Note that one dimension is given in meters, so we need to convert every dimension into the same unit, which is centimeters in this case.

First, convert the third dimension from meters to centimeters: 0.556 meters × 100 cm/m = 55.6 cm. Now, calculate the volume using the formula Volume = length × width × height = 4.30 cm × 2.41 cm × 55.6 cm = 575.716 cm³.

Next, calculate the density using the formula Density = mass/volume = 1050.0 g / 575.716 cm³ ≈ 1.824 g/cm³. After considering significant figures, the density should be reported as 1.8 g/cm³, since the least number of significant figures in the measurements provided is two (for the height dimension).

The answer to the student's question is option b) 1.8 g/cm³.