Question 107

If a metallic cone of radius 30 cm and height 45 cm is melted and recast into metallic spheres of radius 5 cm, find the number of spheres.

Solution

Volume of metallic cone = $$\frac{1}{3} \pi r^2 h$$

= $$\frac{1}{3} \pi * 30^2 * 45 = 13500 \pi cm^3$$

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

= $$\frac{4}{3} \pi * 5^3 = \frac{500 \pi}{3} cm^3$$

=> Required no. of spheres = $$\frac{13500 \pi}{\frac{500 \pi}{3}}$$

= 81

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