A copper sphere has an 18 cm diameter. It is then heated and pulled into a length of wire with a consistent cross section. Find the diameter of the wire if its length is 108 m.

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0.5 cm

0.6 cm

0.7 cm

0.8 cm

answer is B.

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Detailed Solution

It is given that the sphere is 18 cm in diameter.

∴ d = 18 cm ⇒ r = 9 cm

Also, given that the wire is 108 m long.

∴ h = 108 m = 10800 c m

We know that the volume of the sphere is

43 π r 3,

where r is its radius.
The volume of a cylinder is

π r 2 h,

where r is the radius of the base and h is the cylinder's height.
Let’s assume that the radius of the wire is

R .

∴ 43 π × r 3 = π × R 2 × 10800 ⇒ 43 π × 93 = π × R 2 × 10800

⇒ R 2 = 43 π × 729 π × 10800 ⇒ R = 9100 ⇒ R = 0.3 cm

Therefore the diameter of the wire can be calculated as,
Question Image

Therefore the wire has a 0.6 cm diameter.
Hence, option (2) is correct.

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