Question

a student of rectangle student has a rectangular sheet of dimension 14cm into 22 CM he wants to make a cylinder in such a way that volume is minimum find the height of a cylinder​

Answer 1

for minimum volume, the height has to be 22 cm

• Case 1: If he rolls along the length, then it will be the height and the breadth will be the circumference of the cylinder

• So, 2πr = 22  ⇒ 2*22/7 *r = 22  ⇒ r = 7/2  cm
• Volume = pie *r2 * h  = 22/7 * 7/2 * 7/2 * 14  = 539 cubic cm

• Case 2: if he rolls along the breadth, then it will be the height and length will become the circumference.
• so 2*22/7*r = 14  ⇒ r = 49/22  cm
• Volume = 22/7 * 49/22 * 49/22 * 22 = 343 cubic cm

Hence, the 2nd case has the least volume.

So, for minimum volume, the height has to be 22 cm