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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 \mathrm{~cm} $ and height $ 10.5 \mathrm{~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:

Each pen holder was to be of radius $3\ cm$ and height $10.5\ cm$.

There were $35$ competitors.

To do:

We have to find the cardboard that was required to be bought for the competition.

Solution:

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

Height of the pen holder $(h) = 10.5\ cm$

Therefore,

The surface area of the pen holder $=2 \pi r h+\pi r^{2}$

$=\pi r(2 h+r)$

$=\frac{22}{7} \times 3(2 \times 10.5+3)$

$=\frac{66}{7}(21+3)$

$=\frac{66}{7} \times 24$

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

The number of pen holders made $=35$

This implies,

Total area of the cardboard required $=\frac{1584}{7} \times 35$

$=7920 \mathrm{~cm}^{2}$

Therefore,

The total area of the cardboard required is $7920 \mathrm{~cm}^{2}$.

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