Question

What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long? 

(a) 44.0123 cm 

(b) 42.3215 cm 

(c) 44.0625 cm 

(d) 44.6023 cm

Answer 1

(c) 44.0625 cm

Let h be the length (or height) of the solid cylinder 2 cm in diameter.

∴ Volume of solid cylinder = π (1)² h = πh

External radius of hollow cylinder = 6 cm Internal radius of hollow cylinder = 6 cm – 0.25 cm = 5.75 cm 

∴ Volume of the hollow cylinder = π(6² - 5.75²) x 15 

Given,π(6² - 5.75²) x 15 = πh

⇒ (6 + 5.75) (6 – 5.75) × 15 = h 

⇒ h = 11.75 × 0.25 × 15 = 44.0625 cm.