A rectangular tin sheet is 32 cm long and 14 cm wide. It is rolled along its length to form a cylinder, with opposite edges just touching each other. Find the volume (in cm³) of the cylinder.​

Correct option is D

Given:

Length of rectangle (height of cylinder) h = 14cm

Breadth of rectangle (circumference of base) b = 32cm 

Formula Used:

When a rectangle is rolled along its length, the breadth becomes the circumference of the base and length becomes the height.

Circumference of circle =2πr 

Volume of Cylinder = πr²h

Solution: 

Circumference of circle =2πr  = 32 

r = $$\frac{32}{2 \times \pi} = \frac{16}{\pi}$$​​

Now, 

Volume of cylinder = $$\pi \times \left(\frac{16}{\pi}\right)^2 \times 14$$​​

= $$\frac{3584}{\pi} \ cm^3$$​​