Question

OR ( 3727CT )
Ajay needs to cover 10 cylindrical shaped pen stands each of height h cm
and radius r cm using paper. How much paper is required for covering
10 pen stands?

Answer 1

Answer:

As given in the question, pen holders must be made in the shape of a cylinder. One side of the cylinder must be opened and one side must be closed to hold the pens i.e. open at the top and closed at the bottom. So, along with the curved surface area of the cylinder we have to calculate the area of the base. The base of the cylinder will be in a circle. For 35 competitors, the cardboard to be bought should make 35 penholders. So multiply the area of one pen holder with 35 to get the required cardboard area.

Formula used: Curved surface area of the cylinder is 2πrh where ‘r’ is the radius of the base of the cylinder, ‘h’ is the height of the cylinder.

Area of the circle (base) is πr2 where ‘r’ is the radius of the base.

Complete Step-by-step Solution

We are given that the height of the penholder is 10.5cm, base radius of the penholder is 3cm.

We have to calculate the curved surface area of the penholder and the area of the circle (bottom) to get the required cardboard area of a penholder.

Total area of the penholder= Curved surface area of the penholder + Area of the base circle of the penholder.

Which is 2πrh+πr2

π=227,r=3cm,h=10.5cm

Now, substitute the above values in the total area formula.

Total area = 2πrh+πr2

=(2×227×3×10.5)+(227×3×3)=227×3((2×10.5)+3)=667(21+3)=66×247=15847cm2

So, to make one penholder by a competitor we require 15847cm2 of cardboard to be bought.

For 35 competitors, we require 35×15847cm2 of cardboard to make 35 penholders.

→35×15847→355×158471→5×1584→7920cm2

Therefore, 7920 square centimeter of cardboard was required to be bought for the competition conducted by Vidyalaya for 35 competitors.

Note: Curved surface area of the cylinder excludes the bases. While calculating the total required cardboard area, do not add the area of the opened circle i.e. top circle. Another approach to solve this problem is to subtract the area of the top from the total surface area of the pen holder.