# A solid metallic sphere of diameter 21 cm is melted and recast into small cones of diameter 3.5 cm and height 3 cm each.

Question:

A solid metallic sphere of diameter 21 cm is melted and recast into small cones of diameter 3.5 cm and height 3 cm each. Find the number of cones so formed.

Solution:

Radius of sphere $=\frac{21}{2} \mathrm{~cm}$

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

$=\left(\frac{4}{3} \pi \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}\right) \mathrm{cm}^{3}$

Radius of cone $=\frac{3.5}{2} \mathrm{~cm}$

Height of cone $=3 \mathrm{~cm}$

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

$=\left(\frac{1}{3} \pi \times \frac{35}{20} \times \frac{35}{20} \times 3\right) \mathrm{cm}^{3}$

Number of cones $=\frac{\text { Volume of the metallic sphere }}{\text { Volume of each cone }}$

$=\frac{4 \times \pi \times 21 \times 21 \times 3 \times 20 \times 20}{3 \times 2 \times 2 \times 2 \times \pi \times 35 \times 3 \times 3 \times 3}$

$=504$

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