The radius of the base of a right circular cylinder is 5 cm and its volume is 3125 π cm³. A metallic wire of radius 2.5 mm is wrapped around a cylinder so as to cover the curved surface of the cylinder. What will be the length (in m) of the wire?

Given : 

Radius = 5 cm

Volume = 3125π 

Wire of radius = 2.5 mm

Formula Used : 

Volume of Cylinder = πr²h

Curved Surface Area of Cylinder = 2πrh

Calculation : 

We know,

⇒ 1 cm = 10 mm

⇒ 1 m = 100 cm

Voulme of Cylinder = 3125π = πr²h

⇒ 3125 = 25 × h

⇒ h = 125

Now, Radius of Wire = 2.5 mm = 0.25 cm

Diameter of Wire = 5 mm = 0.5 cm

So, number of rows of wire to cover the whole cylinder = Height/Diameter of Wire

So, number of rows of wire to cover the whole cylinder = 125/0.50 = 250

Length covered in one round of wire = 2π × 5 cm

Total Length of the Wire = 250 x (2π × 5) = 2500 π cm = 25 π m

∴ The correct answer is 25π m.