Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

Assertion (A): The number of coins 1.75 cm in diameter and 2 mm thick from a melted cuboid (10 cm × 5.5 cm × 3.5 cm) is 400.

Reason (R): Volume of a cylinder of base radius r and height h is given by V= (πr²h) cubic units. And, area of a cuboid = (l × b × h) cubic units.

Assertion is correct and Reason is correct explanation of the given assertion.

Explanation:

Assertion (A):

Given: A coin which is 1.75 cm in diameter and 2 mm thick.

A cuboid with dimensions (10cm × 5.5cm × 3.5cm)

A coin is in the form of a cylinder.

Volume of the Cylinder is given by: πr²h

Let V₁ be the volume of the coin.

∴ V₁ = πr²h

⇒ V₁ = π × ()² × (here, 1.75 is the diameter,∴ radius = , and 1mm = cm)

⇒ V₁ = π × (0.875)² × 0.2 = cm²

Volume of a cuboid is given by: l × b × h

Let V₂ be the volume of the of the cuboid.

∴ V₂ = l × b × h

⇒ V₂ = 10 × 5.5 × 3.5 = 192.5 cm²

Let ‘n’ be the number of coin melted .

∴ n × V₁ = V₂

⇒ n × = 192.5

⇒ n = 192.5 × = 400

∴ n = 400

That is 400 coin when melted can be moulded into a cuboid of given dimensions.

Reason(R):

Volume of a cylinder of base radius r and height h is given by V= (πr²h) cubic units. And, area of a cuboid = (l × b × h) cubic units.

∴ Assertion is correct and Reason is correct explanation of the given assertion.