Question

a student has rectangular sheet of dimensions 14 cm × 22cm . He wants to make a cylinder in such a way that volume is minimum. Find the height of cylinder

Answer 1

as the formula for volume is πr2h
so radius should be smaller than the height
so the height is 22 with volume as 343cm3
the other way, it's volume was 539

Answer 2

The height of the cylinder is 22 cm.

• The length and breadth of the paper is 14 cm and 22 cm respectively.

• Now, the paper is folded to form a cylinder.

• If we fold the paper around its breadth then the height of the cylinder will be equal to the 14 cm and the circumference of the cylinder will be 22 cm.

Now computing volume using the given data :

2πr = 22

r = 11/π cm.

Now, volume = πr²h

Volume = π(11/π)(11/π)14 = 539 cm³      (Equation 1)

• Now, If we fold the paper around its length then the height of the cylinder will be equal to the 22 cm and the circumference of the cylinder will be 14 cm.

Now computing volume using the given data :

2πr = 14

r = 7/π cm.

Now, volume = πr²h

Volume = π(7/π)(7/π)22 = 343 cm³                  (Equation 2)

• Comparing equation 1 and 2 , we get the minimum value of volume when the paper is folded around its length.

• Therefore, the height of the cylinder will be 22 cm for the cylinder to have minimum volume.