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?

Answers (1)
H Harsh Kankaria

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