Question

1. a bar of soap measures 10cm x 5cm x 3cm and has a mass of 120 g. calculate the density of will it float or sink in the bathtub? explain.

Explanation:

Step1: Calculate the volume of the soap

The volume \( V \) of a rectangular - shaped object (soap in this case) is given by \( V=l\times w\times h \), where \( l = 10\mathrm{cm}\), \(w = 5\mathrm{cm}\), and \(h = 3\mathrm{cm}\).
\(V=10\times5\times3=150\mathrm{cm}^3\)

Step2: Calculate the density of the soap

The density formula is \(D=\frac{m}{V}\), where \(m = 120\mathrm{g}\) and \(V = 150\mathrm{cm}^3\).
\(D=\frac{120\mathrm{g}}{150\mathrm{cm}^3}=0.8\mathrm{g/cm}^3\)

Step3: Determine if the soap will float or sink

The density of water is \(1\mathrm{g/cm}^3\). If an object's density \(D_{object}

Answer:

\(M = 120\mathrm{g}\), \(V=150\mathrm{cm}^3\), \(D = 0.8\mathrm{g/cm}^3\). The soap will float because its density (\(0.8\mathrm{g/cm}^3\)) is less than the density of water (\(1\mathrm{g/cm}^3\)).