Question

the table below lists the masses and volumes of several pieces of the same type of metal. there is a proportional relationship between the mass and the volume of the pieces of metal. determine the volume, in cubic centimeters, of a piece of metal that has a mass of 32.832 grams. round your answer to the nearest tenth.

Explanation:

Step1: Find the density (constant of proportionality)

Since there is a proportional relationship \(m = kV\) (where \(m\) is mass, \(V\) is volume, and \(k\) is the constant of proportionality). Using the first pair of values \(V = 8.6\) and \(m=49.536\), we find \(k=\frac{m}{V}\). So \(k=\frac{49.536}{8.6}=5.76\)

Step2: Use the formula to find the volume

We know \(m = 32.832\) and \(k = 5.76\). From \(m=kV\), we can solve for \(V\). Rearranging the formula gives \(V=\frac{m}{k}\). Substitute \(m = 32.832\) and \(k = 5.76\) into the formula: \(V=\frac{32.832}{5.76}=5.7\)

Answer:

\(5.7\)