What length of solid cylinder 2 cm in diameter must be taken to cast i

1.	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» (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.

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»

(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.