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.

Answer 1

Radius of sphere${\displaystyle =\frac{21}{2}\text{cm}}$

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

${\displaystyle =(\frac{4}{3}\pi \times \frac{21}{2}\times \frac{21}{2}\times \frac{21}{2}){\text{cm}}^3}$

Radius of cone ${\displaystyle =\frac{3.5}{2}\text{cm}}$

Height of cone = 3 cn

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

${\displaystyle =(\frac{4}{3}\pi \times \frac{21}{2}\times \frac{21}{2}\times \frac{21}{2}){\text{cm}}^3}$

Radius of cone${\displaystyle =\frac{3.5}{2} \text{cm}}$

Height of cone = 3 cm

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

${\displaystyle =(\frac{1}{3}\pi \times \frac{35}{20}\times \frac{35}{20}\times 3){\text{cm}}^3}$

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

 

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

= 504