Question

If a rectangular sheet of paper of size $ 14{\rm{cm}} \times 8{\rm{cm}} $ is rolled to form a cylinder, then which of the following are true?
THIS QUESTION HAS MULTIPLE CORRECT OPTIONS
(A) Radius of cylinder will be $ 14{\rm{cm}} $ and height will be $ 8{\rm{cm}} $ .
(B) Radius of cylinder will be $ 8{\rm{cm}} $ and height will be $ 14{\rm{cm}} $ .
(C) If the circumference of base will be $ 14{\rm{cm}} $ then height will be $ 8{\rm{cm}} $ .
(D) If the circumference of base is $ 8{\rm{cm}} $ then its height will be $ 14{\rm{cm}} $ .

Answer 1

Hint: If a cylinder is made from rolling a rectangular sheet of paper, then the dimensions of the cylinder made would depend on the side of the rectangular paper from which it is rolled, but there is no change in volume or total surface area.

Complete step-by-step answer:
Given:
The dimension of the rectangular sheet of paper is given below-
The length of the paper $ l = 14{\rm{cm}} $
And, the width of the paper $ w = 8\;{\rm{cm}} $
Now, if this paper is rolled along its width to form a cylinder, then the circumference of the base of the cylinder formed would be equal to the width of the paper and the height of the cylinder would be equal to the length of the paper.

Then, the circumference of the base of cylinder is equal to width of the paper
$\Rightarrow$ Circumference of the base of cylinder $ = 8\;{\rm{cm}} $

And, the height of the cylinder is equal to the length of the paper.
$\Rightarrow$ The height of the cylinder $ = 14{\rm{cm}} $
Similarly,
Now, if the paper is rolled along its length to form a cylinder, then the circumference of the base of the cylinder formed would be equal to the length of the paper and the height of the cylinder would be equal to the width of the paper.
So, circumference of the base of cylinder = Length of the paper
$\Rightarrow$ Circumference of the base of cylinder $ = 14{\rm{cm}} $
And, the height of the cylinder is equal to width of the paper
$\Rightarrow$ The height of the cylinder $ = 8\;{\rm{cm}} $
Therefore, the correct options are-
(C) If the circumference of base will be $ 14{\rm{cm}} $ then height will be $ 8{\rm{cm}} $ .
(D) If the circumference of base is $ 8{\rm{cm}} $ then its height will be $ 14{\rm{cm}} $ .

So, the correct answer is “Option C AND D”.

Note: The circumference of the base of the cylinder is different for both cases, which means that the radius of the base of the cylinder would be different for each case. For example, if the circumference of the base is $ 14{\rm{cm}} $ , then its radius will be-
The circumference of the base $ = 2\pi r $
(where $ r $ is the radius of the base of the cylinder)
  $
\Rightarrow 2\pi r = 14\\
\Rightarrow r = \dfrac{7}{\pi }
 $
And if the circumference of the base is $ 8\;{\rm{cm}} $ then its radius would be,
  $
\Rightarrow 2\pi r = 8\\
\Rightarrow r = \dfrac{4}{\pi }
 $