Question

The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 2 2/3cm, find the diameter of the cylinder.

Answer 1

The diameter of the cylinder is 14 cm

Step-by-step explanation:

Given as :

The diameter of internal hollow spherical shell = d = 10 cm

So, The radius of internal hollow spherical shell = r = $\dfrac{d}{2}$ = $\dfrac{10}{2}$ = 5  cm

The diameter of external hollow spherical shell = D = 6 cm

So, The radius of external hollow spherical shell = R = $\dfrac{D}2}$ = $\dfrac{6}{2}$ = 3 cm

Volume of hollow spherical shell = V = $\dfrac{4}{3}$ × π × (r³  - R³)

Or,                                                      V = $\dfrac{4}{3}$ × π × ( 5³ - 3³ )

Or,                                                      V = $\dfrac{4}{3}$ × 3.14 × 98

Or,                                                      V = 410.293  cm³

Again

The hollow spherical shell melted and recast into a solid cylinder

The length of cylinder = h = 2 $\dfrac{2}{3}$  = $\dfrac{8}{3}$  cm

Let The Radius of cylinder = R' cm

Now,

Volume of cylinder = π × R'² × h

Or,                         v = 3.14 × R'² × $\dfrac{8}{3}$

As The  hollow spherical shell melted and recast into a solid cylinder

So, Volume of hollow spherical shell = Volume of cylinder

Or,  V = v

Or,   410.293  cm³  = 3.14 × R'² × $\dfrac{8}{3}$

Or, 410.293  cm³  = 8.373 × R'²

∴   R'² = $\dfrac{410.293}{8.373}$

Or  R'² = 49

i.e R' = √49

Or,  R' = 7 cm

So, The Radius of cylinder = R' = 7 cm

Therefore , The diameter of cylinder = D' = 2 × R' =  2 × 7 = 14 cm

Hence, The diameter of the cylinder is 14 cm . Answer