Question

A rectangular piece of paper 11cm by 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.
(a) 38.5 cm³
(b) 40.5 cm³
(c) 41.5 cm³
(d) 42.5 cm³

Answer 1

Hint: In this problem, a rectangular piece of paper is folded into a cylinder so the base circle radius can be evaluated by equating the length of the rectangle to perimeter. The height of the cylinder is the breadth of the rectangle. Since we have a radius and height of the cylinder, we can evaluate the volume.

Complete step-by-step answer:
According to the question, the length and breadth of a rectangular piece of paper is 11 cm and 4 cm respectively. Also, the height of the cylinder generated is 4 cm which shows the rectangular piece of paper is folded along its breadth.
Let r be the radius of the circular portion of the base of the cylindrical piece. Since, the perimeter of the base circle of the cylinder is equal to the length of the rectangle.
So, by the formula of circumference of the circle we get,
$\begin{align}
  & 2\pi r=11 \\
 & r=\dfrac{11}{2\pi } \\
 & r=\dfrac{11\times 7}{2\times 22}=\dfrac{7}{4}cm \\
\end{align}$
Therefore, the radius of the base circle is $\dfrac{7}{4}$cm.
Now, the volume of the cylinder is $\pi {{r}^{2}}h\text{ c}{{\text{m}}^{3}}$. Now, putting values in the volume formula we get,
$\begin{align}
  & V=\dfrac{22}{7}\times \dfrac{7}{4}\times \dfrac{7}{4}\times 4 \\
 & V=\dfrac{77}{2}=38.5c{{m}^{3}} \\
\end{align}$
Hence, the volume of the cylinder is 38.5 cm³.
Hence, option (a) is correct.

Note: The key step for solving this problem is the knowledge of volume of a cylinder. If we want to generate a cylinder out of a rectangular piece of paper along breadth, then breadth becomes height of the cylinder and length becomes the perimeter of the base circle of the cylinder. By using this fact, we calculated the volume of the cylinder.