Q1.1CYL Check Your Learning (a) To three... [FREE SOLUTION]

Chapter 1: Q1.1CYL (page 9)

Check Your Learning (a) To three decimal places, what is the volume of a cube \(\left( {c{m^2}{\rm{ }}} \right)\) with an edge length of \(0.843{\rm{ }}cm\)? (b) If the cube in part (a) is copper and has a mass of \(5.34{\rm{ }}g,\) what is the density of copper to two decimal places

Expert verified

a. The volume of a cube\(\left( {c{m^2}{\rm{ }}} \right)\) with an edge length of \(0.843{\rm{ }}cm\) is \(0.599c{m^3}\).

b. If a cube having volume \(0.599c{m^3}\) is copper and has a mass of \(5.34{\rm{ }}g,\)then the density of copper is \(8.91\,g/c{m^3}\).

The edge length of the cube =\(0.843{\rm{ }}cm\)

Volume of cube

\(\begin{aligned}{} = 0.843cm \times 0.843cm \times 0.843cm\\ = 0.599\,c{m^3}\end{aligned}\)

Hence the volume of the cube is \(0.599c{m^3}\).

From the above step, we have the volume of the copper cube\( = 0.599c{m^3}\)

We know that\({\rm{density}} = \frac{{{\rm{mass}}}}{{{\rm{volume}}}}\)

\(\begin{aligned}{} &= \frac{{5.34g}}{{0.599c{m^3}}}\\ &= 8.91g/c{m^3}\end{aligned}\)

Hence the density of the copper cube is \(8.91g/c{m^3}\).

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