Question

a solid sphere of radius 18 cm is melted down and drawn out into a long cylindrical wire of uniform thickness 6mm. find the length of the wire.​

Answer 1

Hi,

Here is your answer

Given:

Radius of sphere(R)=18cm

Thickness of wire=Diameter(d)=6mm=0.6cm

To find:

Length of wire (l)

Solution:

Radius of wire(r)=d/2=0.3cm

Here since the sphere is coverted into wire, which is a cylinder

Volume of sphere=Volume of cylinder

4/3×π×R³=πr²h

Cancelling π on both sides

4/3×R³=h×r²

Here height of the cylinder is the length of the wire

h=l

Hence

l×r²=4/3×R³

Substituting the given datas

We get,

l×(0.3)²=4/3×18³

l=7776/0.009

l=864000cm

Notes:

1. Remember to convert all the given datas to the same units before calculating.

2. Volume of a sphere=4/3×π×R³

3. Volume of a cylinder=πr²h

Hope this helpps you.

Answer 2

Answer:

864

Step-by-step explanation: