Question

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 $3cm$ and height $10.5cm$. 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?

Answer 1

Given:

$R=3$cm, $H=10.5$cm

$\Rightarrow$Surface area $=$ Curved Surface Area $+$ Base Area

$=2\pi rh+\pi r^2$

$=2\times \frac{22}{7}\times 3\times \frac{10.5}{10}+\frac{22}{7}\times 3\times 3$cm${}^2$

$=198+\frac{198}{7}$cm${}^2$

$=\frac{1584}{7}$cm${}^2$

$\Rightarrow$Area of cardboard sheet used by competitor $=\frac{1584}{7}$cm${}^2$

$\Rightarrow$Area of cardboard sheet used by $35$ competitors $=\frac{1584}{7}\times 35$

$=7920$cm${}^2$