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? [Assume $\pi =\frac{22}{7}$]

Answer 1

Radius (r) of the circular end of cylindrical pen holder $=3cm$

Height (h) of penholder $=10.5cm$

Surface area of $1$ penholder $=$ CSA of penholder $+$ Area of base of penholder

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

$=\left[\right(2\times \frac{22}{7}\times 3\times 10.5)+(\frac{22}{7}\times \left(3{)}^2\right)]c{m}^2$

$=[132\times 1.5+\frac{198}{7}]c{m}^2$

$=[198+\frac{198}{7}]c{m}^2$

$=\frac{1584}{7}c{m}^2$

Area of cardboard sheet used by $1$ competitor $=\frac{1584}{7}c{m}^2$

Area of cardboard sheet used by $35$ competitors

$=[\frac{1584}{7}\times 35]c{m}^2=7920c{m}^2$

Therefore, $7920c{m}^2$ cardboard sheet will be bought.