Question

1. the density of water is 1 gram per \\(\mathrm{cm}^3\\). an object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. will a toy in the shape of a rectangular prism that is 1 centimeter by 2 centimeter by 2 centimeter with mass 3 grams sink or float? explain your reasoning.

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Explanation:

Step1: Calculate the volume of the rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Given \(l = 1\space cm\), \(w=2\space cm\), \(h = 2\space cm\), then \(V=1\times2\times2=4\space cm^{3}\).

Step2: Calculate the density of the toy

The density formula is \(
ho=\frac{m}{V}\). Given \(m = 3\space g\) and \(V = 4\space cm^{3}\), then \(
ho=\frac{3}{4}= 0.75\space g/cm^{3}\).

Step3: Compare the density of the toy with the density of water

The density of water is \(1\space g/cm^{3}\). Since \(0.75\space g/cm^{3}<1\space g/cm^{3}\).

Answer:

The toy will float because its density (\(0.75\space g/cm^{3}\)) is less than the density of water (\(1\space g/cm^{3}\)).