Question

The radius of a sphere is 9 cm . It is melted and drawn into a wire of diameter 2mm. Find the length of wire in cm

Answer 1

Answer:

291600 mm                  

Step-by-step explanation:

Radius of sphere = 9 cm

1 cm = 10 mm

So, 9 cm = 90 mm

Diameter of wire = 2 mm

Radius = Diameter /2 = 2/2 = 1 mm

Since The sphere is melted into wire so volume will remain same .

Volume of sphere = 4/3 pie r^3

               

Since wire is in the form of cylinder.

So, formula of volume of cylinder =  

                              =

Since The sphere is melted into wire so volume will remain same .

⇒            4 x (90)^3 

⇒         291600 mm

Hence the length of wire is 291600 mm

Answer 2

Answer:

Let R = radius of the sphere

Now, R = 9 cm

volume of sphere, V1 = 43πR3 = 43π(9)3 = 972π cm3

volume of sphere, V1 = 43πR3 = 43π93 = 972π cm3

Now, diameter of the wire  = 2 mm = 0.2 cm       [as 1 cm = 10 mm]

radius of the wire, r = 0.1 cm

Let h = length of the wire

volume of cylindrical wire, V2 = πr2h = (0.1)2πh cm3

volume of cylindrical wire, V2 = πr2h = 0.12πh cm3

Since the sphere is melted and recast into wire, so in this case volume of the material remains same.

So, V2 = V1

⇒(0.1)2πh = 972π⇒0.01 h = 972

⇒h = 97200 cm

⇒h = 972 m            [as, 1m = 100 cm]