Question

A rectangular piece of paper is 22cm long and 10cm wide. A cylinder is formed by rolling the paper along its length. Find the volume of the cylinder.
$
  {\text{A}}{\text{. 175c}}{{\text{m}}^3}{\text{ }} \\
  {\text{B}}{\text{. 75c}}{{\text{m}}^3}{\text{ }} \\
  {\text{C}}{\text{. 125c}}{{\text{m}}^3}{\text{ }} \\
  {\text{D}}{\text{. 275c}}{{\text{m}}^3}{\text{ }} \\
$

Answer 1

Hint: In this question on forming a cylinder from a rectangular piece of paper the length of the rectangular piece is the height of the cylinder and the width of the rectangular piece is the circumference of the cylinder.

Complete step-by-step answer:
Height of cylinder $(h)$= 22cm eq.1
 Circumference of cylinder=$2\pi r = 10{\text{cm}}$
$ \Rightarrow r = \dfrac{5}{\pi }$ eq.2
Now, the volume of cylinder=$\pi {r^2}h$ eq.3
Put values of r and h from eq.1, eq,2 in eq.3 we get
the volume of cylinder $ = \pi {(\dfrac{5}{\pi })^2} \times 22 \\
   = (\dfrac{{25}}{\pi }) \times 22 \\
$
Put $\pi = \dfrac{{22}}{7}$ in above equation, we get
Then, Volume of cylinder $ = 25 \times 7 \\
   = 175{\text{c}}{{\text{m}}^3} \\
 $
Hence, option A is correct.

Note: Whenever we get this type of problem the key concept is to have knowledge about how different shapes are formed from other simpler shapes like in this case a cylinder is formed by rolling a rectangular piece and their formulas too.