Question

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 is

its answer is this but can you explain me how? ans--- 6 (19) raise to the power 1/3

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$<b><i>The Diameter of a spherical shell is 6(19)⅓ cm.</b>$

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

$<b>Volume of spherical shell = Volume of right circular cylinder </b>$

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  

$<b>r³  = 513 cm </b>$

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.

$<b>Hence, the Diameter of a spherical shell = 6(19)⅓ cm.</b>$

HOPE THIS ANSWER WILL HELP YOU….