Question

1. a sample of iron in the shape of a rectangular prism has the dimensions of 2 cm × 3 cm × 2 cm. if the mass of this object is 94 g, what is the density of iron?

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume \( V \) of a rectangular prism is \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Given \( l = 3\space cm \), \( w = 2\space cm \), \( h = 2\space cm \), so \( V = 3\times2\times2 \).
\( V = 12\space cm^3 \)

Step2: Calculate the density

The formula for density \(
ho \) is \(
ho=\frac{m}{V} \), where \( m \) is mass and \( V \) is volume. Given \( m = 94\space g \), \( V = 12\space cm^3 \), so \(
ho=\frac{94}{12} \).
\(
ho\approx7.83\space g/cm^3 \) (rounded to two decimal places)

Answer:

The density of iron is approximately \( 7.83\space g/cm^3 \) (or exactly \( \frac{47}{6}\space g/cm^3\approx7.83\space g/cm^3 \))