Q. 785.0( 1 Vote )

# 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.A. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).B. Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).C. Assertion (A) is true and Reason (R) is false.D. Assertion (A) is false and Reason (R) is true.

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.

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