Question

The diameter of a brass sphere is 6 cm. It is melted and stretched onto a long wire of uniform circular cross-section. If the length of the wire is 36 cm, then find the diameter of the wire.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\huge\mathfrak{Solution:}$

Here, diameter of the sphere = 6 cm

Therefore, radius of the sphere r1 = 3 cm

Length of the wire = 36 cm (given)

Suppose radius of the wire = r cm

Since wire in cylindrical shape is casted on melting the sphere

Therefore, volume of the sphere = volume of the wire in cylindrical shape of radius r

Therefore, 4/3 × pi × r1^3 = pi × r^2 × h

or 4/3 × r1^3 = r^2 × h

or 4/3 × (3)^3 = r^2 × 36

or r^2 = 4 × 9 / 36 = 1

Therefore, r = root 1 = 1 cm

Hence, diameter of the wire = 2 × r = 2 × 1 cm = 2 cm

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