Question

1. a bar of soap is 12 cm tall, 6 cm wide, and 10 cm long. it has a mass of 415 grams. what is the density of the bar of soap.
2. a sheet of metal is 2 cm wide, 10 cm tall, and 15 cm long. it was 4 grams. what is the density?

Explanation:

Step1: Calculate the volume of the soap bar

The volume \(V\) of a rectangular prism (the shape of the soap bar) is given by \(V = l\times w\times h\), where \(l = 10\ cm\), \(w=6\ cm\), and \(h = 12\ cm\).

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Step2: Use the density formula

The density formula is \(
ho=\frac{m}{V}\), where \(m = 415\ g\) (mass) and \(V = 720\ cm^{3}\) (volume).

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Step3: Calculate the volume of the metal sheet

For the metal sheet, \(l = 15\ cm\), \(w = 2\ cm\), \(h = 10\ cm\).

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Step4: Use the density formula for the metal sheet

Given \(m = 4\ g\) and \(V = 300\ cm^{3}\), \(
ho=\frac{m}{V}\)

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Answer:

The density of the soap bar is approximately \(0.58\ g/cm^{3}\) and the density of the metal sheet is approximately \(0.013\ g/cm^{3}\)