Question

a solid metallic sphere of diameter 8cm is melted and drawn ito a cylindrical wire of uniform width. If the legth of the wire is 12m, find its width.

Answer 1

It might help you.

Answer 2

Answer:

5.32m

Step-by-step explanation:

Diameter of sphere = 8m

Radius of sphere = Diameter/2 = 8/2 =4 m

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

                              = $\frac{4}{3} \pi (4)^{3}$

                              = $\frac{4}{3} \pi \times 64$

Length of wire is 12 m

Since wire is in the shape of cylinder

Volume of wire :$\pi r^{2} h$

                           $\pi r^{2} \times 12$

Since Sphere is melted to make wire so, volume will remain same .

$\frac{4}{3} \pi \times 64=\pi r^{2} \times 12$

$\frac{4}{3} \times 64=r^{2} \times 12$

$85.33=r^{2} \times 12$

$\frac{85.33}{12}=r^{2}$      

$7.11=r^{2}$                

$\sqrt{7.11}=r$  

$2.66=r$  

Radius of wire = 2.66m

Width = Diameter = Radius *2 = 2.66*2  =5.32 m

Hence the width of the wire is 5.32 m