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Option 2 : Quantity A < Quantity B

Quantity A:

Volume of the wire (in cylindrical shape) = Volume of the sphere. 

⇒ π × (16)2 × h = (4/3) × π × (12)3 

⇒ 256h = 2304

⇒ h = 9 cm

Quantity B:

Given the area of the trapezium = 285 cm2 and height = 15 cm;

We know that:

Area of the trapezium = ½ × (Sum of parallel sides) × Height

⇒ 285 = ½ × (Sum of parallel sides) × 15

⇒ (Sum of parallel sides) = 38 cm

Given the ratio of length of two parallel sides is 10 : 9;

∴ Length of longer side of the two parallel sides = 38 × 10/19 = 20 cm

∴ Quantity A < Quantity B

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