The radii of internal and external surfaces of a hollow spherical shel

1.	The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.
Answer» Let r₁ and r₂ be the internal and external base radii of spherical shell. r₁ = 3 cm, and r₂ = 5 cm Base radius of solid cylinder, r = 7 cm Let the height of the cylinder = h As per given statement: The hollow spherical shell is melted into a solid cylinder, so Volume of solid cylinder = Volume of spherical shell πr²h = 4/3 π(r₂³ – r₁³) ⇨ 49h = 4/3(125 – 27) or h = 8/3 cm

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

Answer»

Let r₁ and r₂ be the internal and external base radii of spherical shell.

r₁ = 3 cm, and r₂ = 5 cm

Base radius of solid cylinder, r = 7 cm

Let the height of the cylinder = h

As per given statement:

The hollow spherical shell is melted into a solid cylinder, so

Volume of solid cylinder = Volume of spherical shell

πr²h = 4/3 π(r₂³ – r₁³)

⇨ 49h = 4/3(125 – 27)

or h = 8/3 cm