Question

A copper sphere of diameter 6cm is melted and drawn into 36cm long wire of uniform circular cross section. Then, its radius is

Answer 1

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Answer 2

The radius of wire is 1 cm

Step-by-step explanation:

Diameter of sphere = 6 cm

Radius of sphere =$\frac{6}{2} = 3 cm$

Volume of sphere =$\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (3)^3$

Length of wire = 36 cm

Let the radius of wire be R

Volume of cylinder = $\pi r^2 h = \frac{22}{7} \times R^2 \times 36$

$\pi \times R^2 \times 36 = \frac{4}{3} \pi (3)^3\\R^2 \times 36 = \frac{4}{3}(3)^3\\R^2=\frac{\frac{4}{3}(3)^3}{36}\\R=\sqrt{\frac{\frac{4}{3}(3)^3}{36}}\\R=1$

Hence The radius of wire is 1 cm

#Learn more:

The diameter of a metallic sphere is 6cm. its melted and drawn into a wire having diameter of cross section 0.2cm find the length of the cross section

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