A rectangular tin sheet is 12 cm long and 5 cm broad. It is rolled along its length to form a cylinder by making the opposite edges just touch each other. The volume of the cylinder (in cm³) is :

1. $\dfrac{60}{π}$

2. $\dfrac{100}{π}$

3. $\dfrac{120}{π}$

4. $\dfrac{180}{π}$

For cylinder, rolled along its length:

Height of cylinder, h = 5 cm

Radius of cylinder be r cm

Circumference of base = 2πr = 12

$\Rightarrow 2 \times π \times \text{r} = 12 \\[1em] \Rightarrow \text{r} = \dfrac{12}{2π} \\[1em] \Rightarrow \text{r} = \dfrac{6}{π} \text{ cm.}$

Volume of cylinder = πr²h

$= π \times \Big(\dfrac{6}{π}\Big)^2 \times 5 \\[1em] = π \times \Big(\dfrac{36}{π^2}\Big) \times 5 \\[1em] = \dfrac{180}{π} \text{ cm}^3$

Hence, option 4 is the correct option.