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On the day of her examination, Riya sharpened her pencil from both ends as shown below: The diameter of the cylindrical and conical part of the pencil is $4.2$ mm. If the height of each conical part is $2.8$ mm and length of entire pencil is $105.6$ mm, find the total surface area of the pencil.
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$d = 4.2$ mm, $r = 2.1$ mm. Height of cylindrical part $(h) = 100$ mm. Height of conical part = $2.8$ mm. Slant height $(l) = \sqrt{(2.8)^2 + (2.1)^2} = 3.5$ mm. Curved Surface Area of Cylinder = $2 \times \frac{22}{7} \times 2.1 \times 100 = 1320$ mm$^2$. Curved Surface Area of Cone = $\frac{22}{7} \times 2.1 \times 3.5 = 23.1$ mm$^2$. Total Surface Area of pencil = Curved Surface Area of cylinder + Curved Surface Area of two cones = $1366.2$ mm$^2$.