The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm.

It is given that

Radius of the circular part of the penholder (r) = 3 cm

The height of the penholder (h) = 10.5 cm

Surface area of one penholder (S.A)

= Curved surface area of penholder + Area of the circular base of penholder

$=2 \pi r h+\pi r^{2}$

$=(2 * 3.14 * 3 * 10.5)+3.14 * 3^{2}$

= 198 + 198/7

$=1584 / 7 \mathrm{~cm}^{2}$

The total area of cardboard sheet used by one competitor $=1584 / 7 \mathrm{~cm}^{2}$

The total area of cardboard sheet used by 30 competitors $=1584 / 7 * 35 \mathrm{~cm}^{2}$

$=7920 \mathrm{~cm}^{2}$

Therefore, the school needs to buy $7920 \mathrm{~cm}^{2}$ 2 of cardboard sheet for the competition.