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 ?
This questions was previously asked in
2024 CDS -1 MATH
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.
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By: Parvesh Mehta