The length of a wire (in m) of 0.5mm radius that can be drawn after melting a solid copper sphere of diameter 12cm is:
- A11500
- B1152
- C1150
- D11520
Solution & Step-by-step Explanation
The volume of the sphere equals the volume of the cylindrical wire.
1. Volume of Sphere:
Diameter=12cm⟹Radius (R)=6cm
Volume of Sphere=
3
4
πR
3
=
3
4
π(6)
3
=
3
4
π×216=288πcm
3
2. Volume of Cylindrical Wire:
Radius (r)=0.5mm=0.05cm
Let the length of the wire be h (in cm).
Volume of Cylinder=πr
2
h=π(0.05)
2
h=0.0025πhcm
3
3. Equating Volumes:
288π=0.0025πh
288=
10000
25
h
h=
25
288×10000
=288×400=115200cm
4. Convert to meters:
Length in meters=
100
115200
=1152m
1. Volume of Sphere:
Diameter=12cm⟹Radius (R)=6cm
Volume of Sphere=
3
4
πR
3
=
3
4
π(6)
3
=
3
4
π×216=288πcm
3
2. Volume of Cylindrical Wire:
Radius (r)=0.5mm=0.05cm
Let the length of the wire be h (in cm).
Volume of Cylinder=πr
2
h=π(0.05)
2
h=0.0025πhcm
3
3. Equating Volumes:
288π=0.0025πh
288=
10000
25
h
h=
25
288×10000
=288×400=115200cm
4. Convert to meters:
Length in meters=
100
115200
=1152m