From a circular metal plate of radius 7 cm and thickness 0·16 mm, a sector is cut off containing an angle 150°. The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm?

Remaining area fraction = (360-150)/360 = 210/360 = 7/12 of full circle. Volume of remaining piece = (7/12) × π × 7² × 0.016 = (7/12) × π × 49 × 0.016 cm³. Setting equal to (4/3)π r³: r³ = (3/4) × (7/12) × 49 × 0.016 = (7 × 49 × 0.016)/16 = 5.488/16 = 0.343. So r = ∛0.343 = 0.7 cm.