Using it's formula, it is found that the surface area of the mug that is painted blue is of 36.13 square inches.
The surface area of a cylinder of radius r and height h is given by:
[tex]S = 2\pi r(r + h)[/tex]
Half of this area is inside the cylinder, and half is outside.
In this problem, the inside of the mug is blue, with r = 2 and h = 3.75, hence:
[tex]S_b = \pi r(r + h) = 2\pi(2 + 3.75) = 36.13[/tex]
The surface area of the mug that is painted blue is of 36.13 square inches.
More can be learned about the surface area of a cylinder at https://brainly.com/question/14657844
