Q

# 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 cm and height 10.5 cm.

Q : 11     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 $\small 3\hspace{1mm}cm$ and height  $\small 10.5\hspace{1mm}cm$. 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?

Views

Given, a cylinder with a base.

The radius of the cylinder = $r = 3\ cm$

Height of the cylinder = $h = 10.5\ cm$

We know,

The lateral surface area of a cylinder of radius $r$ and height  $h$ = $2\pi r h$

$\therefore$  Area of the cylindrical penholder = Lateral areal + Base area

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

$= \frac{22}{7}\times3\times[2(10.5)+3]$

$\\ = \frac{22}{7}\times3\times[24] \\ \\ = \frac{1584}{7}\ cm^2$
Area of 35 penholders  = $\frac{1584}{7}\times35\ cm^2$

$= 7920\ cm^2$

Therefore, the area of carboard required is $7920\ cm^2$

Exams
Articles
Questions