Question

a spherical lead ball of diameter 24 cm is melted and recast into three spherical lead balls of radius 6 cm and 8 cm find the diameter of the third ball​

Answer 1

Step-by-step explanation:

In this case the volume of the initial spherical ball will be the sum of the volumes of the new three balls.

Volume of a sphere =

3

4

πr

3

As the diameter of the given sphere is 3cm then its radius =

2

3

=1.5cm ......... as [radius=

2

diameter

The radius of other two balls will be .75cm and 1cm.

Let the radius of the third new ball be Rcm.

Volume of the three new sphere = Volume of old sphere

⇒

3

4

π.75

3

+

3

4

π.1

3

+

3

4

π.R

3

=

3

4

π1.5

3

⇒ .75

3

+ 1

3

+ R

3

= 1.5

3

⇒ 0.421875+1+R

3

=3.375

⇒ 1.421875+R

3

=3.375

⇒ R

3

=1.953125

⇒ R=1.953125

3

1

⇒ R=1.25

So, the radius of the third new ball is 1.25cm .

Therefore, the diameter =2.5 cm

Answer 2

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