Question

1. a block of wood that measures 3.0 cm on each side has a mass of 27 g. what is the density of the block?

Explanation:

Step1: Calculate the volume of the block

The block is a cube (since each side is 3.0 cm). The volume \( V \) of a cube is given by \( V = s^3 \), where \( s \) is the length of a side.
So, \( s = 3.0 \, \text{cm} \), then \( V=(3.0\,\text{cm})^3 = 27\,\text{cm}^3 \). (Note: \( 1\,\text{cm}^3 = 1\,\text{mL} \), but we'll use \( \text{cm}^3 \) for density calculation as density unit can be \( \text{g/cm}^3 \))

Step2: Recall the density formula

Density \(
ho \) is defined as mass \( m \) divided by volume \( V \), so \(
ho=\frac{m}{V} \).

Step3: Substitute the values

We know \( m = 27\,\text{g} \) and \( V = 27\,\text{cm}^3 \). Substituting into the formula: \(
ho=\frac{27\,\text{g}}{27\,\text{cm}^3} \).

Step4: Calculate the density

Simplifying the fraction, \( \frac{27}{27}=1 \), so the density is \( 1\,\text{g/cm}^3 \) (or \( 1\,\text{g/mL} \) since \( 1\,\text{cm}^3 = 1\,\text{mL} \)).

Answer:

The density of the block is \( 1\,\text{g/cm}^3 \) (or \( 1\,\text{g/mL} \)).