Question

if the diameter of a metallic sphere is 6cm it melted and a wire of diameter 0.2cm is drawn then the length of the wire made shall be​

Answer 1

$\red{\textbf{Answer :- 3600cm}}$

Step-by-step explanation:

$\red{\textbf{We have}}$

$\textsf{Diameter of metallic sphere =6cm}$

$\textsf{Radius of metallic sphere =3cm}$

$\textsf{Also we have}$

$\textsf{Diameter of cross-section of cylindrical}$

$\textsf{wire=0.2cm}$

∴$\textsf{Radius of cross-section fo cylindrical}$

$\textsf{wire=0.1cm}$

$\textsf{Let the length of the wire be h cm}$

$\textsf{Since the metallic sphere is converted}$

$\textsf{into a cylindrical shaped wire of length}$

$\textsf{h cm}$

$\textsf{Volume of the metal used in wire= Volume}$

$\textsf{of the sphere}$

$= \pi \times {r}^{2} \times h$

$= \LARGE\frac{4}{3}\small \times \pi \times {r}^{3}$

$= \pi \times {(0.1)}^{2} \times h = \LARGE\frac{4}{3} \small \times \pi \times 27$

$= \pi \times \LARGE \frac{1}{100} \small\times h = 36\pi$

$= h = \LARGE \frac{3\pi \times 100}{\pi}$

$= 3600cm$

$\textsf{=36metres}$

∴$\textsf{Length of the wire=3600cm}$