Question

A solid sphere of radius $$15\ cm$$ is melted and react into solid right circular cones of radius $$2.5\ cm$$ and height $$8\ cm$$. Calculate the number of cones recast.

Solution

Radius of a solid sphere, $$r=15\ cm$$Volume of a solid sphere $$=\displaystyle\frac{4}{3}\pi r^3$$$$=\displaystyle\frac{4}{3}\times \pi (15)^3\ cm^3$$.Now, radius of right circular cone $$=2.5\ cm$$ and height, $$h=8\ cm$$.Volume of right circular cone $$=\displaystyle\frac{1}{3}\pi r^2h$$$$=\displaystyle\frac{1}{3}\pi (2.5)^2\times 8$$$$\therefore$$ The number of cones $$=\displaystyle\frac{\text{Volume of a sphere}}{\text{Volume of a cone}}$$$$=\displaystyle\frac{\displaystyle\frac{4}{3}\pi \times (15)^3}{\displaystyle\frac{1}{3}\pi (2.5)^2\times 8}$$$$=\displaystyle\frac{15\times 15\times 15}{2.5\times 2.5\times 2}$$$$=270$$.Mathematics

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