The number of square inches of tin required for the construction is [tex]73.01 \ in^2[/tex]
Explanation:
From the figure, we can see that the radius of the cylinder is
[tex]r=1 \frac{1}{2} \ in=\frac{3}{2} \ in[/tex]
Also, the height of the cylinder is
[tex]h=6 \frac{1}{4} \ in = \frac{25}{4} \ in[/tex]
The number of square inches of tin required for the construction can be determined using the formula for surface area of the cylinder.
[tex]$S A=2 \pi r(r+h)$[/tex]
Substituting the values of r and h in the above formula, we have,
[tex]$S A=2 \pi (\frac{3}{2}) (\frac{3}{2}+\frac{25}{4})$[/tex]
Adding the terms within the bracket by taking LCM
Thus, we have,
[tex]$S A=2 \pi (\frac{3}{2}) (\frac{6+25}{4})$[/tex]
Simplifying the terms, we get,
[tex]$S A=3 \pi (\frac{31}{4})$[/tex]
[tex]$S A=\frac{93 \pi}{4}[/tex]
Substituting the value [tex]\pi=3.14[/tex], we get,
[tex]$S A=\frac{93(3.14)}{4}[/tex]
Multiplying, we have,
[tex]$S A=\frac{292.02}{4}[/tex]
Dividing, we get,
[tex]SA=73.005 \ in^2[/tex]
Rounding off to two decimal places, we have,
[tex]SA= 73.01 \ in^2[/tex]
Thus, the number of square inches of tin required for the construction is [tex]73.01 \ in^2[/tex]
