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

For Wire :

Radius (r) = 5mm = 0.5 cm

Length (h) = 42$$\frac{2}{3}$$ m = $$\frac{128}{3\times\ 100}$$ cm

For Sphere ;

Radius (R) ?

As we know

If the shape of a substance is change by melting then Volume of old figure should be equal to volume of new figure.

i.e; Volume of wire = Volume of Sphere

i.e; $$\pi\ r^2h\ =\ \frac{4}{3}\pi\ R^3$$

$$\therefore\ \ \frac{\left(0.05^2\times\ 128\right)\times\ 100}{3}\ =\ \frac{4}{3}\ R^3$$

$$\therefore\ \ \left(0.05\times\ 0.05\times\ 32\right)\times\ 100\ =\ R^3$$
$$\therefore\ \ R^3=8$$

$$\therefore\ \ R^{ }=2cm$$

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SSC MTS 22nd August 2019 Shift-2

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?

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