A copper Spherical ball of diameter 240 m. is melted and molded to form wire of length 4 km. What should be the diameter of Wire?
Answer
Correct Answer : b ) 48 m
Explanation :According to the question,
The spherical ball has been used to form cylindrical wire.
We know that, Volume of the material would remain same, i.e., Volume of Spherical ball = Volume of Cylindrical wire.
Let the radius of wire be R, radius of ball be r and height of the cylinder be h.
Diameter of Spherical ball = 240 m
Radius of the ball, r = \(240 \over 2\)=120 m
Length of Cylindrical wire = h = 4 km
⇒ h = 4000 m
We know that
Volume of Sphere=\({4 \over 3}πr^3\)
The sphere is melted and recasted into the wire of cylindrical shape
Volume of Cylinder = πr2h
Where ‘r’ and ‘h’ are the radius and height of the cylinder, respectively.
Volume of Spherical ball = Volume of cylindrical wire
⇒\({4 \over 3}πr^3 =πR^2h\)
Substituting the values
\({4 \over 3}π*120*120*120=π*R^2*4000\)
⇒ R2 = 576
⇒ R = 24m
Diameter of wire = 2 * 24 m
⇒ 48 m
Hence, (b) is the correct answer.
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