Question

Find the thickness of a spherical shell whose outer diameter is 12cm, if it weighs 7/8 times as much as a solid ball of the same diameter. The volume of the solid ball of diameter 12cm is 4/3π6³cm³.

Answer 1

Given,

Outer Diameter of spherical shell and ball = 12cm => Radius = 6cm

Volume of solid ball = 4/3π6³

Volume of shell = (7/8) Volume of Solid Ball - (1)

To find,

Thickness of spherical shell = Outer Radius - Inner Radius

Solution,

We can simply solve this by using the following mathematical process.

First, let us find the volume of the spherical shell. r₁ is outer radius and r₂ is inner radius.

=> Volume of shell = 4/3πr₁³ - 4/3πr₂³

                               = 4/3π6³ - 4/3πr₂³

Let's equate this to the volume of solid ball - from (1)

4/3π6³ - 4/3πr₂³ = (7/8) 4/3π6³

=> 4/3π6³ - (7/8) 4/3π6³  = 4/3πr₂³

=> 1/6π6³ = 4/3πr₂³

=> 36π = 4/3πr₂³ => r₂³ = 27 => r₂ = 3

∴ Thickness of the shell = r₁-r₂ = 6-3 = 3cm

Hence, we have the thickness of the spherical shell as 3cm.