A rectangular piece of paper 10 cm by 8 cm is rolled along its width to get the cylinder of largest size. The curved surface area of the cylinder formed is :

1. 44 cm²

2. 20 cm²

3. 80 cm²

4. 80 cm²

Clearly, width of the rectangular sheet = Circumference of the base of the cylinder

The circumference of a circle = 2πr

⇒ 2πr = 8

$⇒ 2 \times \dfrac{22}{7} \times r = 8\\[1em] ⇒ \dfrac{44}{7} \times r = 8\\[1em] ⇒ r = \dfrac{7\times 8}{44} \\[1em] ⇒ r = \dfrac{56}{44} \\[1em] ⇒ r = \dfrac{14}{11}$

Height of the cylinder formed = Length of the sheet

⇒ h = 10 cm

Curved surface area of cylinder = 2πrh

$= 2 \times \dfrac{22}{7} \times \dfrac{14}{11} \times 10 cm^2\\[1em] = \dfrac{44}{7} \times \dfrac{14}{11} \times 10 cm^2\\[1em] = \dfrac{616}{77} \times 10 cm^2\\[1em] = \dfrac{6160}{77} cm^2\\[1em] = 80 cm^2$

Hence, option 3 is the correct option.