Question

A solid metallic sphere of radius 12 cm is melted and recast into a number of small cones, each of radius 4 cm and height 3 cm. Find the number of cones so formed.

Answer 1

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Answer 2

Answer: There are 144 cones so formed.

Step-by-step explanation:

Since we have given that

Radius of metallic sphere = 12 cm

Radius of small cone = 4 cm

Height of small cone = 3 cm

So, Volume of metallic sphere is given by

$\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\times \frac{22}{7}\times 12\times 12\times 12$

And volume of cone is given by

$\frac{1}{3}\pi r^2h\\\\=\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3$

So, Number of cones so formed is given by

$\frac{\text{Volume of sphere}}{\text{Volume of cone}}\\\\=\frac{\frac{4}{3}\times \frac{22}{7}\times 12\times 12\times 12}{\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3}\\\\=144\ cones$

Hence, there are 144 cones so formed.