Question 75

A metallic sphere of diameter 40 cm is melted into smaller spheres of radius 0.5 cm. How many such small balls can be made?

Solution

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

radius of sphere = diameter/2 = 40/2 = 20 cm

volume of sphere = total volume of all smaller sphere

$$\frac{4}{3} \pi 20^3 = n \times \frac{4}{3} \pi (0.5)^3$$

8000 = 0.125n

n = 8000/0.125 = 64000

$$\therefore$$ 64000 small balls can be made.

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