106k views
1 vote
9. The radii of three lead balls are 5 cm, 8 cm and 12 cm. The three balls are melted into one

ball. What is the radius of this new ball?

User YnkDK
by
7.7k points

1 Answer

5 votes

Answer:

Step-by-step explanation:

Radius of first spherical ball =

2

2

cm=1cm

Radius of second spherical ball =

2

2

3

14.5

cm=

3

14.5

cm

Let the radius of the third ball be r cm.

Radius of the main spherical ball =

2

5

cm=2.5cm

Volume of main spherical ball = Volume of spherical ball 1+Volume of spherical ball 2+ Volume of spherical ball 3

Volume of a sphere =

3

4

πr

3

So,

3

4

π×2.5

3

=

3

4

π1

3

+

3

4

π(

3

14.5

)

3

+

3

4

πr

3

⇒2.5

3

=1

3

+(

3

14.5

)

3

+r

3

⇒r

3

=15.625−1−14.5

⇒r

3

=0.125=0.5×0.5×0.5

⇒r=0.5

User Louis Simoneau
by
8.1k points