Question

The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius $3cm$ and height $10.5cm$. The Vidyalaya was to supply to the competitors with cardboard. If there were $35$ competitors, how much cardboard was required to be bought for the competition?

Answer 1

Radius fo cylindrical pen holder $\left(r\right)=3cm$

Height $\left(h\right)=10.5cm$

Since, the pen holder is open at the top, but covered at the bottom.

So, surface area of one penholder $=$Curved surface area of cylinder $+$ Area of bottom circle

$\therefore$ Surface area of the pen holder $=2\pi rh+\pi r^2=\pi r(2h+r)$

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

=$\frac{66}{7}(21+3)=\frac{66}{7}\times 24c{m}^2$

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

$\therefore$ Number of pen holders made $=35$

$\therefore$ Total of cardboard required $=\frac{1584}{7}\times 35=1584\times 5=7920c{m}^2$