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Question 64
A copper wire of radius 0.5 mm and length $$42\frac{2}{3}$$ m is melted and converted into a sphere of radius R cm. What is the value of R?
Solution
$$\therefore\ \ \left(0.05\times\ 0.05\times\ 32\right)\times\ 100\ =\ R^3$$
$$\therefore\ \ R^3=8$$
$$\therefore\ \ R^{ }=2cm$$
For Wire :Â
Radius (r) = 5mm = 0.5 cm
Length (h) = 42$$\frac{2}{3}$$ m =Â $$\frac{128}{3\times\ 100}$$ cm
For Sphere ;Â
Radius (R) ?Â
As we knowÂ
If the shape of a substance is change by melting then Volume of old figure should be equal to volume of new figure. Â
i.e; Volume of wire = Volume of SphereÂ
i.e;Â $$\pi\ r^2h\ =\ \frac{4}{3}\pi\ R^3$$
$$\therefore\ \ \frac{\left(0.05^2\times\ 128\right)\times\ 100}{3}\ =\ \frac{4}{3}\ R^3$$$$\therefore\ \ \left(0.05\times\ 0.05\times\ 32\right)\times\ 100\ =\ R^3$$
$$\therefore\ \ R^3=8$$
$$\therefore\ \ R^{ }=2cm$$
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