Chemistry: Molecular Approach (4th Edition)

Published by Pearson
ISBN 10: 0134112830
ISBN 13: 978-0-13411-283-1

Chapter 1 - Exercises - Page 40: 120


\[\underline{\text{0}\text{.77 in}}\]

Work Step by Step

Calculate volume of aluminum as follows: \[\begin{align} & V=\frac{m}{d} \\ & =\frac{\text{85 g}}{\text{2}\text{.7 g/c}{{\text{m}}^{3}}} \\ & =31.48\text{ c}{{\text{m}}^{3}} \end{align}\] Calculate volume of cylinder as follows: \[\begin{align} & V=\frac{4}{3}\pi {{r}^{3}} \\ & r={{\left( \frac{3V}{4\pi } \right)}^{1/3}} \\ & ={{\left( \frac{\left( 3 \right)\left( 31.48\text{ c}{{\text{m}}^{3}} \right)}{\left( 4 \right)\left( 22/7 \right)} \right)}^{^{1/3}}} \\ & =1.958\text{ cm} \end{align}\] Radius is in centimeter (cm); convert it into inches (in) as follows: \[\begin{align} & 1\text{ cm}=\text{0}\text{.3937 in} \\ & \text{1}\text{.958 cm}=\left( \text{1}\text{.958 cm} \right)\left( \frac{\text{0}\text{.3937 in}}{1\text{ cm}} \right) \\ & =0.77\text{ in} \end{align}\]
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