Question

A metallic cone of radius 12cm and height 24cm is melted
and made into sphere of radius 2 cm each. How many spheres are formed
​

Answer 1

Given:-

• Radius of metallic cone = 12 cm
• Height of the metallic cone = 24 cm
• Radius of each sphere = 2 cm

To Find:-

• How many sphere are formed.

Solution:-

Let us first find the volume of the metallic cone.

For cone,

Radius = 12 cm

Height = 24 cm

We know,

Volume of cone = $\sf{\dfrac{1}{3}\pi r^2 h}$

Therefore,

Volume = $\sf{\dfrac{1}{3}\times \dfrac{22}{7}\times (12)^2\times 24}$

Volume = $\sf{\dfrac{1}{3}\times \dfrac{22}{7}\times 12\times 12\times 24}$

Volume = $\sf{\dfrac{22}{7}\times 12\times 12\times 8}$

Volume = $\sf{\dfrac{25344}{7}}$

Volume = $\sf{3620.6\:cm^3}$

Now,

We need to find the volume of sphere.

For sphere,

Radius = 2 cm

We know,

Volume of sphere = $\sf{\dfrac{4}{3}\pi r^3}$

Therefore,

Volume = $\sf{\dfrac{4}{3}\times\dfrac{22}{7}\times (2)^3}$

Volume = $\sf{\dfrac{4}{3}\times\dfrac{22}{7}\times 8}$

Volume = $\sf{\dfrac{704}{21}}$

Volume = 33.5 cm³

Number of cubes formed:-

$\sf{\dfrac{Volume\:of\:cone}{Volume\:of\:sphere}}$

= $\sf{\dfrac{3620.6}{33.5}}$

= $\sf{108\:\:\:[Approx]}$

Therefore number of spheres so formed is 108 [Approximately]

______________________________________

Formulas Used:-

• Volume of sphere = 4/3 πr³ cu.units.
• Volume of cone = 1/3πr²h cu.units.

______________________________________