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.