Question

A solid gold ball of radius 7 cm was melted and then drawn into wire of diameter 0.2 cm. Find the length of the wire ?

Answer 1

hope you understand

Answer 2

Answer:

The length of wire is 457.33 m

Step-by-step explanation:

Given,

radius of lead ball = 7 cm

Diameter of wire = 0.2 cm

Since we know,

Diameter = 2 *  radius

radius = Diameter / 2

radius = 0.2 / 2

radius of wire = 0.1

Now,

Since the ball is melted and drawn into wire

So,

Volume of ball ( Sphere ) = Volume of wire ( Cylinder )

Volume of sphere = $\frac{4}{3} \pi r^{3}$

Volume of cylinder = $\pi r^{2} h$

Let the length of wire be ' l '

So,

$\frac{4}{3} \pi r^{3}$ =  $\pi r^{2} h$

Substituting the values,

$\frac{4}{3} \pi 7^{3}$ =  $\pi 0.1^{2} l$

Dividing by $\pi$ on both the sides,

$\frac{4}{3} *(7^{3} )$ = $0.1^{2} * l$

$\frac{4}{3} * 343$ = 0.01 l

457.33 = 0.01 l

l = 457.33 / 0.01

l = 45733.33 cm

Since,

1 cm = 0.01 m

So,

45733.33 cm = 45733.33 * 0.01 = 457.33 m

Hence,

The length of wire is 457.33 m