# 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. 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?

**Solution:**

The curved surface area of a right circular cylinder of base radius 'r' and height 'h' is 2πrh and total surface area =2πr(r + h).

So, the total amount of cardboard required will be the product of the surface area of pen holders and the total number of participating students.

Area of cardboard required for each penholder = 2πrh + πr² = πr(2h + r)

Area of cardboard required for 35 penholders = 35 × πr (2h + r )

Radius of the penholder, r = 3 cm

Height of the penholder, h = 10.5 cm

Area of cardboard required for 35 penholders

= 35 × πr(2h + r )

= 35 × 22/7 × 3 cm × (2 × 10.5 cm + 3 cm)

= 330 cm × 24 cm

= 7920 cm²

7920 cm² of cardboard will be required for the competition.

**Video Solution:**

## 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. 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?

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.2 Question 11:

**Summary:**

It is given that 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. If there were 35 competitors, we have found that 7920 cm² of cardboard was required to be bought for the competition.