Math, asked by BrainlyHelper, 1 year ago

A spherical shell of lead, whose external diameter is 18 cm, is melted and. recast into a right circular cylinder, whose height is 8 cm and diameter 12. cm. The internal diameter of the shell.

Answers

Answered by nikitasingh79
5

Answer:

The Diameter of a spherical shell is 6(19)⅓ cm.

Step-by-step explanation:

SOLUTION :  

Let internal Radius of a shell be r

External diameter of a spherical shell = 18 cm

External radius of a spherical shell, R = 18/2 = 9 cm

Height of a right circular cylinder , h = 8 cm

Diameter of a right circular cylinder  = 12cm

Radius of a right circular cylinder ,r1 = 12/2 = 6 cm

Volume of spherical shell = Volume of right circular cylinder

4/3π(R³ - r³) = πr1²h

4/3(9³ - r³)  = 6² × 8

4/3(729 - r³)  = 36 × 8

729 - r³ = (36 × 8 × 3) / 4

729 - r³ = 9 × 24

729 - r³ = 216

729 - 216 =  r³  

r³  = 513 cm

r = ³√ 27 × 19

r = 3³√19

r = 3(19)⅓ cm  

Internal Radius of a spherical shell = 3(19)⅓ cm  

Diameter of a spherical shell =  2 × Radius = 2 × 3(19)⅓ cm = 6(19)⅓ cm.

Hence, the Diameter of a spherical shell = 6(19)⅓ cm.

HOPE THIS ANSWER WILL HELP YOU….

Answered by Harshikesh16726
0

Answer:

Volume of spherical shell = Volume of cylinder

3

4

π(R

1

3

−R

2

3

)=πr

2

h⇒

3

4

(9

3

−R

2

3

)=6

2

×8

⇒729−R

2

3

=

4

36×8×3

=216⇒R

2

3

=729−216=513

⇒R

2

=

3

513

=3(19)

1/3

cm

∴ internal diameter of shell =2×3(19)

1/3

=6(19)

1/3

cm

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