Question

What length of solid cyclinder 2 cm in diameter must be taken to recast into a hhollow cyclinder of ecternal diameter 20 cm, 0.25 cm thick and 15 cm long?

Answer 1

Hello!

Here is your answer!
==========================================================

Given diameter of solid cylinder = 2 cm


Radius of solid cylinder, r = 1 cm


Volume of solid cylinder =  πr2h

= π × 12 × h = πh →  (1)

Length of hollow cylinder, H = 16 cm


External diameter = 20 cm


External radius = 10 cm


Thickness = 2.5 mm = 0.25 cm


Internal radius = 10 – 0.25 = 9.75 cm


Volume of hollow cylinder  = π[102 – (9.75)2] × 16


= 16π × 19.75 × 0.25 →  (2)


From (1) and (2), we get


Πh = 16π × 19.75 × 0.25

  
∴ h = 16 × 19.75 × 0.25 = 79 cm 
==========================================================

Hope it helps!