Question

What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?

Answer 1

External diameter of hollow cylinder = 20 cm 

Therefore, radius = 10 cm 

Thickness = 0.25 cm 

Hence, Internal radius = (10 – 0.25) = 9.75 cm 

Length of cylinder (h) = 15 cm 

∴ Volume = πh(R² – r²)

= π × 15(10² – 9.75²)

= 15π(100 – 95.0625) cm³

= 15π × 4.9375 cm³

Diameter = 2 cm

Therefore, radius (r) = 1 cm 

Let h be the length

Then, volume = πr²h = π(1 × 1)h = πh

Now, according to given condition: 

πh = 15π × 4.9375

`=>` h = 15 × 4.9375

`=>` h = 74.0625

Length of cylinder = 74.0625 cm