Question

A solid metallic sphere of diameter 21 cm is melted and recast
into a number of smaller cones, each of d'ameter 3.5 cm and
height 3um find the number of cone so formed.​

Answer 1

Answer:

number of cone to be formed = 378cones

Step-by-step explanation:

Answer 2

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Given:

A solid metallic sphere of diameter 21cm is melted and recast into a number of smaller cones, each of diameter 3.5cm and height 3cm.

To find:

The number of cone formed.

Explanation:

Let the number of cone formed be R.

We have,

The sphere of diameter= 21cm

∴Radius of the sphere= $\frac{21}{2} cm$

We know that formula of the volume of sphere: $\frac{4}{3} \pi r^{3}$

Volume of sphere=$\frac{4}{3} *\frac{22}{7} *(\frac{21}{2} )^{3}$

Volume of sphere= $(\frac{88}{21} *\frac{21}{2} *\frac{21}{2} *\frac{21}{2} )cm^{3}$

Volume of sphere= $(\frac{\cancel{88}}{\cancel{21}} *\frac{\cancel{21}*21*21}{\cancel{8}} )cm^{3}$

Volume of sphere= (11×21×21)cm³

Volume of sphere= 4851cm³.

Now,

Given, diameter of cone= 3.5cm

∴Radius of the cone= $\frac{3.5*10}{2*10} =\frac{35}{20} cm$

Radius of the cone=$\frac{\cancel{35}}{\cancel{20}} = \frac{7}{4} cm$

• Height of the cone= 3cm

Formula of the volume of cone: $\frac{1}{3} \pi r^{2} h$ [cubic unit]

Volume of the cone= $(\frac{1}{3} *\frac{22}{7} *\frac{7}{4} *\frac{7}{4} *3)cm^{2}$

Volume of the cone= $(\frac{1}{\cancel{3}}*\frac{22}{\cancel{7}} *\frac{\cancel{7}}{4} *\frac{7}{4} *\cancel{3})cm^{3}$

Volume of the cone= $\frac{22*7}{4*4} cm^{3}$

According to the question:

⇒ R × volume of cone= volume of sphere

⇒ R× $\frac{22*7}{4*4} cm^{3} = 4851cm^{3}$

⇒ R= $\frac{\cancel{4851}*16}{22*\cancel{7}}$

⇒ R= $\frac{\cancel{693}*16}{\cancel{22}}$

⇒ R= (31.5× 16) cone

⇒ R= 504 cone.

Thus,

The number of cone so formed is 504.