Question

A sports company was ordered to prepare $ 100 $ paper cylinders for packing shuttlecocks. The required dimensions of the cylinder are $ 35\;cm $ length height and its radius is $ 7\;cm $ . Find the required area of thick paper sheet needed to make $ 100 $ cylinders?

Answer 1

Hint: In this type of problem we use a unitary method. In this we first find the area required to make one cylinder by substituting value of given r and h of cylinder in formula and then using area so obtained multiplying by $ 100 $ to get the total area required to make $ 100 $ cylinder which are required for shuttlecocks.
Formulas used: Surface area of cylinder $ 2\pi rh $ , where r is radius and h is height or length of cylinder.

Complete step-by-step answer:
Given dimension of the cylinder are:
Radius of cylinder is = $ 7\;cm $
Height or length of cylinder is = $ 35\;cm $
Also, we know that the surface area of cylinder or curved surface area of cylinder is given as: $ 2\pi rh $ , where r is radius and h is height or length of the cylinder.
 $ \Rightarrow Surface\,\,area\,\,of\,\,cylinder = 2\pi rh $
Substituting values in above formula. We have,
\[
  Surface\,area = 2 \times \dfrac{{22}}{7} \times 7 \times 35 \\
   \Rightarrow Surface\,area = 2 \times \dfrac{{22}}{{{7}}} \times{7} \times 35 \\
   \Rightarrow Surface\,area = 2 \times 22 \times 35 \\
   \Rightarrow Surface\,area = 44 \times 35 \\
   \Rightarrow Surface\,area = 1540 \;
 \]
Therefore, from above we see that the surface area of the cylinder is $ 1540\,c{m^2} $ .
Since, it is required to make $ 100 $ such a cylinder.
Therefore, total sheet of paper required to make $ 100 $ cylinders given as: $ 100 \times \,\,surface\,\,area\,\,of\,\,one\,\,cylinder $
 $
   = 100 \times 1540 \\
   = 154000 \;
  $
Hence, we see that the total area required to make $ 100 $ cylinders for packing shuttlecocks is $ 154000\,c{m^2} $ .
So, the correct answer is “ $ 154000\,c{m^2} $ ”.

Note: In case of mensuration problem one must see whether terms are having the same units or not. If any term having different units then first convert or write in the same unit and then choose appropriate mensuration formula corresponding to given figure/figures and finally doing calculation carefully as any silly mistake may lead to wrong answer.