The students of a 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. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?

Given :
Radius (r) of the circular end of cylindrical penholder = 3 cm
Height (h) Of penholder = 10.5 cm

We have,

Surface area of 1 penholder
= CSA of penholder + Area of base of penholder
= \(2{\pi}rh\) + \({\pi}{r}^2\)
= [\(2 × \frac{22}{7} × 3 × 10.5 + \frac{22}{7} × {3}^2 {cm}^2\)]
= [\(132 × 1.5 + \frac{198}{7} {cm}^2\)]
= \(198 + \frac{198}{7} {cm}^2\)
= \(\frac{1584}{7} {cm}^2\)

So, we get,

Area Of cardboard sheet used by 1 competitor = \(\frac{1584}{7} {cm}^2\)

Thus, Area of cardboard sheet used by 35 competitors
= \((\frac{1584}{7} × 35) {cm}^2\) = 7920 \({cm}^2\)

\(\therefore \) 7920 \({cm}^2\) cardboard sheet will be bought for the competition.