Question

a bar of soap is 12 cm tall, 6 cm wide, and 10 cm long. it has a mass of 360 grams. what is the density of the bar of soap? options: 2g/cm³, 0.25g/cm³, 0.5g/cm³, 4g/cm³

Explanation:

Step1: Calculate the volume of the soap bar

The soap bar is a rectangular prism, and the volume \( V \) of a rectangular prism is given by the formula \( V = length \times width \times height \). Here, length \( l = 10 \, \text{cm} \), width \( w = 6 \, \text{cm} \), and height \( h = 12 \, \text{cm} \). So, \( V=10\times6\times12 \).
\( V = 720 \, \text{cm}^3 \)

Step2: Calculate the density of the soap bar

Density \(
ho \) is defined as mass \( m \) divided by volume \( V \), i.e., \(
ho=\frac{m}{V} \). We know that \( m = 360 \, \text{g} \) and \( V = 720 \, \text{cm}^3 \). So, \(
ho=\frac{360}{720} \).
\(
ho = 0.5 \, \text{g/cm}^3 \)

Answer:

\( 0.5 \, \text{g/cm}^3 \) (corresponding to the option "0.5g/cm³")