A rectangular sheet of 31.4 cm x 10 cm size is rolled across its length to make a cylinder without overlap. What will be the approximate volume of the cylinder?

Correct option is A

Given:
A rectangular sheet of 31.4 cm (length) and 10 cm (width)
It is rolled along its length → the length becomes the circumference of the cylinder
The width becomes the height of the cylinder

Formula:

$$\text{Circumference} = 2\pi r, \quad \text{Volume of cylinder} = \pi r^2 h \\[8pt]$$​

Solution:

​$$2\pi r = 31.4 \Rightarrow r = \frac{31.4}{2\pi} = \frac{31.4}{6.28} = 5 \, \text{cm} \\$$

$$\text{Volume} = \pi \times 5^2 \times 10 = \pi \times 25 \times 10 = 250\pi \\$$

$$\text{Volume} \approx 3.14 \times 250 = 785 \, \text{cm}^3$$

Correct Answer: (A) 785 cm³​​​​​