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 17.8\( \ mm\). If the height of each conical part is 6\( \ mm\) and length of entire pencil is \(105.6 \ mm\), find the total surface area of the pencil. [Use \(\pi = \frac{22}{7}\)]
Slant height of conical part \(l =\)
Area of the pencil \(=\) ______________ \(sq. mm\)