Answer
(a)\[\underline{1.9\times \text{1}{{\text{0}}^{4}}\text{ g and 3}\text{.0}\times \text{1}{{\text{0}}^{3}}\text{ g }}\]
(b) Yes
Work Step by Step
(a)
The volume of a cylinder is as follows:
\[\begin{align}
& V=\pi {{r}^{2}}h \\
& =\left( \frac{22}{7} \right){{\left( 3.8\text{ cm} \right)}^{2}}\left( 22\text{ cm} \right) \\
& =998.4\text{ c}{{\text{m}}^{3}}
\end{align}\]
Calculate mass as follows:
\[m=dV\]
Mass of gold cylinder will be as follows:
\[\begin{align}
& m=\left( 19.3\text{ g/c}{{\text{m}}^{3}} \right)\left( \text{998}\text{.4 c}{{\text{m}}^{3}} \right) \\
& =1.9\times {{10}^{4}}\text{ g}
\end{align}\]
Mass of sand cylinder will be as follows:
\[\begin{align}
& m=\left( \text{3}\text{.0 g/c}{{\text{m}}^{3}} \right)\left( \text{998}\text{.4 c}{{\text{m}}^{3}} \right) \\
& =3.0\times {{10}^{3}}\text{ g}
\end{align}\]
Mass of gold cylinder and that of sand cylinder are \[\underline{1.9\times \text{1}{{\text{0}}^{4}}\text{ g and 3}\text{.0}\times \text{1}{{\text{0}}^{3}}\text{ g }}\].
(b)
The mass of sand is \[\text{3}\text{.0}\times \text{1}{{\text{0}}^{3}}\text{ g}\] and that of gold cylinder is \[1.9\times \text{1}{{\text{0}}^{4}}\text{ g}\].
Yes, the thief sets off the alarm
