A rectangular sheet of paper of length 33 cm and breadth 22 cm is folded in two ways in the form of cylinder. find the difference in the volume of cylinder formed π = 22 by 7.
Answers
The difference in the volume of two cylinders formed by a rectangular sheet of length 33 cm and breadth 22 cm is 635.344 cm³.
• Given,
Length of the rectangular sheet = 33 cm
Breadth of the rectangular sheet = 22 cm
• The sheet can be folded in two ways, either along the length or along the breadth.
• If the sheet is folded along the length,
height of the cylinder (h) = length of the sheet
=> Height of the cylinder (h) = 33 cm
Circumference of the base of the cylinder = breadth of the sheet
=> 2πr = 22 cm
=> 2 × (22/7) × r = 22 cm
=> r = (22 cm × 7) / (2 × 22)
=> r = 7/2 cm
• Volume of the cylinder (V) = πr²h
=> V = π × (7/2 cm)² × 33 cm
=> V = π × (7 × 7 × 33) cm³ / (2 × 2)
=> V = 404.25 π cm³
• If the sheet is folded along the breadth,
Height of the cylinder (h') = breadth
=> Height of the cylinder (h') = 22 cm
• Circumference of the base of the cylinder = length of the sheet
=> 2πr' = 33 cm
=> 2 × (22/7) × r' = 33 cm
=> r' = (33 cm × 7) / (2 × 22)
=> r' = 21/4 cm
• Volume of the cylinder (V') = πr'²h'
=> V' = π × (21/4 cm)² × 22 cm
=> V' = π × (21 × 21 × 22) cm³ / (4 × 4)
=> V' = 606.375 π cm³
• Difference in volumes of both the cylinders = V' - V
=> Difference = 606.375 π cm³ - 404.25 π cm³
=> Difference = 202.155 π cm³
=> Difference = 202.155 × (22/7) cm³
=> Difference = 635.344 cm³