Question

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 $3cm$ 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

Base diameter of frame $=20cm$

So, the base radius of frame $=\frac{20}{2}=10cm$

Surface area of a penholder = CSA of pen holder + Area of base of penholder

$\begin{array}{rcl}2\pi rh+\pi r^2& =& 2\times \left(\frac{22}{7}\right)\times 3\times 10.5+\left(\frac{22}{7}\right)\times {\left(3\right)}^2\\ & =& 198+28.28\\ & =& 226.28c{m}^2\end{array}$

Total area of Cardboard required to be bought for the competition

= Number of competitors x cardboard required for one penholder

$$\begin{gathered} =35\times 226.28 \\ =7919.99\approx 7920c{m}^2 \end{gathered}$$

Hence, cardboard was required to be bought for the competition is $7920c{m}^2$.