UP Police Constable Exam Model Paper 2

Given:
Radius of the sphere is 9 cm = 0.09 m
Diameter of the wire is 2 mm = 0.002 m
Concept Used:
If r be the radius, then volume of the sphere is (4/3)$\mathrm{\pi }{\mathrm{r}}^3$
If r be the radius and h be the length of the wire, then volume of the wire is $\mathrm{\pi }{\mathrm{r}}^2\mathrm{h}$
Calculation:
Volume of the sphere of radius 9 cm is (4/3)π × (0.09)${}^3$ = $0.000972\mathrm{\pi }$ m${}^3$
Diameter of the wire 2 mm = 0.002 m
⇒ Radius of the wire is 0.001 m
Let, the length of the wire is h
Volume of the wire is π(0.001)${}^2$ × h = $\mathrm{\pi }\mathrm{h}$/1000000 m${}^3$
Accordingly,
$0.000972\mathrm{\pi }$ = $\mathrm{\pi }\mathrm{h}$/1000000
⇒ h = 972
∴ The length of the wire in meters is 972 m.