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
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….
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