We will have that the lateral area will be the following:
*First, we can see that if we were to cut a straight vertical line and unfold the label, we would get a rectangle, thus the surface area of the label will be given by:
[tex]S_A=h\cdot C[/tex]Here h is the height of the label and C is the circumference of the base, that is:
[tex]S_A=h\cdot2\pi r[/tex]Now, we determine the radius of the base, that is:
[tex]r=\frac{2.6}{2}\Rightarrow r=1.3[/tex]Now, we replace the values and solve for the surface area:
[tex]\Rightarrow S_A=(4)\cdot(2)\pi(1.3)\Rightarrow S_A\approx32.7[/tex]So, the surface area of the label on the can is approximately 32.7 squared inches.
