Answer
The first cylindrical can that is the can have dimensions of diameter and height as and respectively has more capacity to contain soup. Accordingly, a buyer should purchase first can instead of the second can.
Work Step by Step
The diameter and height of the cylinder is \[6\text{ inches}\] and \[5\text{ inches}\] respectively. The volume of the cylinder will be computed by multiplying the square of the radius with the height and finally multiplying the resultant with the value of pie.
Firstly, compute the radius of the first cylindrical can using the equation as shown below:
\[\begin{align}
& \text{Radius}=\frac{\text{1}}{\text{2}}\times \text{Diameter} \\
& =\left( \frac{1}{2}\times 6 \right)\text{ inches} \\
& =3\text{ inches}
\end{align}\]
Compute the volume of the first cylindrical can using the equation as shown below:
\[\begin{align}
& \text{Volume of the first can (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 3\text{ in}\text{.} \right)}^{2}}5\text{ in}\text{.} \right) \\
& =45\pi \text{ in}{{\text{.}}^{3}}
\end{align}\]
Now, compute the radius of the second cylindrical can using the equation as shown below:
\[\begin{align}
& \text{Radius}=\frac{\text{1}}{\text{2}}\times \text{Diameter} \\
& =\left( \frac{1}{2}\times 5\text{ in}\text{.} \right) \\
& =2.5\text{ in}\text{.}
\end{align}\]
Compute the volume of the second cylindrical can using the equation as shown below:
\[\begin{align}
& \text{Volume of the second can}\left( V \right)=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 2.5\text{ in}\text{.} \right)}^{2}}5\text{ in}\text{.} \right) \\
& =31.25\pi \text{ in}{{\text{.}}^{\text{3}}}
\end{align}\]
