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# 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.