Question : A solid copper sphere of radius 6 cm is melted and redrawn into a wire, whose radius of cross-section is 8 cm. Find the length of the wire.
Option 1: 9 cm
Option 2: 2.25 cm
Option 3: 4.5 cm
Option 4: 6 cm
Correct Answer: 4.5 cm
Solution :
The volume of the copper sphere and the copper wire will be the same, as the sphere is melted and redrawn into the wire.
The volume of a sphere $ = \frac{4}{3}\pi r^3$
The volume of a cylinder $ = \pi R^2 h$
Where $R$ is the radius of the base of the cylinder and $h$ is the height (or length) of the cylinder.
Given: r = 6 cm and R = 8 cm
The volume of the sphere = the volume of the cylinder.
$⇒\frac{4}{3}\pi (6)^3 = \pi (8)^2 h$
$⇒h= 4.5$
Hence, the correct answer is 4.5 cm.
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