Mathematics

Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :
(i) shorter side
(ii) longer side.

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(i) When paper is rolled along shorter side then height = 44 cm and circumference = 33 cm.

⇒ Circumference = 33 cm

⇒ 2πr = 33

⇒ $2 \times \dfrac{22}{7} \times r = 33$

⇒ r = $\dfrac{33 \times 7}{2 \times 22}$ = 5.25 cm.

Volume = πr²h

= $\dfrac{22}{7} \times (5.25)^2 \times 44$

= $\dfrac{22}{7} \times 27.56 \times 44$

= $\dfrac{26680.5}{7}$ = 3811.5 cm³.

Hence, volume of cylinder = 3811.5 cm³.

(ii) When paper is rolled along longer side then height = 33 cm and circumference = 44 cm.

⇒ Circumference = 44 cm

⇒ 2πr = 44

⇒ $2 \times \dfrac{22}{7} \times r = 44$

⇒ r = $\dfrac{44 \times 7}{2 \times 22}$ = 7 cm.

Volume = πr²h

= $\dfrac{22}{7} \times (7)^2 \times 33$

= $\dfrac{22}{7} \times 49 \times 33$

= 5082 cm³.

Hence, volume of cylinder = 5082 cm³.

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