Explanation:

Correct option 2: 0.7 cm

Given:

Radius of circular plate (R) = 7 cm

Thickness of plate (h) = 0.16 mm = 0.016 cm

Angle of the sector (θ) = 150°

Concept:

The volume of the remaining piece after cutting the sector is equal to the volume of the spherical bead formed. Formula used:

Volume of the sector of a cylinder = ( θ/360) π R²h

Volume of the sphere = (4/3) π r³

Solution:

Volume of the sector cut off:

=> (150/360) × π x(7)² × 0.016

=> (5/12) × π x 49 × 0.016

=> 1.026 cm3

Volume of the remaining piece:

=> Total volume of the plate - Volume of the sector cut off

=> π x R²xh-1.026

=>? × 49 × 0.016 - 1.026

=> 3.14 × 0.784 - 1.026

=>2.46176-1.026

=> 1.43576 cm3

Volume of the spherical bead: => (4/3)π r³= 1.43576

=> r³ = (1.43576 × 3)/(4xπ)

=> r³ = 0.3427 cm3 = 0.343 cm3

=> r = ³√0.343

=> r = 0.7 cm

.. The value of r is 0.7 cm.