a solid sphere of diameter 6 cm is melted and drawn into a wire of radius 4mm . find the length of the wire .....
Answers
6 cm =60 mm.
Volume of sphere= 4/3πr3
= 4/3 ×22/7 × 60×60×60. =905142.85mm2.
Volume of cylinder = 905142.85
πr2h = 905142.85
22/7 × 4×4× h = 905142.85
h= 18,000 mm
1mm=1/10cm
18000=18000/10 cm
= 1800 cm.
h= 1,800 cm
Given : A solid sphere of diameter 6 cm is melted and drawn into a wire of radius 4mm.
To find : The length of the wire.
Solution :
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the length of the wire)
Now,
The diameter of solid sphere
= 6 cm
= (6 × 10) mm [As, 1 cm = 10 mm]
= 60mm
So,
The radius of the solid sphere :
= Diameter ÷ 2
= (60 ÷ 2) mm
= 30 mm
Now,
The volume of the solid sphere :
= ⁴/₃ × π × (radius)³
= ⁴/₃ × π × (30)³
= 36000π mm³
Let, the length of the wire = l mm
The volume of the wire :
= π × (radius)² × length
= π × (4)² × l
= 16πl mm³
(Here, the wire is treated as a cylindrical object. The length of the wire is the height of the cylinder and the radius of the wire is the radius of base of the cylinder. Hence, the formula for calculating the volume of cylinder has been applied.)
Now, the volume of the solid sphere and the volume of the wire will be equal. As, the wire is made from the solid sphere itself.
So,
16πl = 36000π
16 × π × l = 36000 × π
16 × l = 36000
l = 36000/16
l = 2250
So, the length of the wire = 2250 mm = (2250 ÷ 10) cm = 225 cm [As, 10 mm = 1 cm]
(This will be considered as the final result.)
Hence, the length of the wire is 225 cm.