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Question

Assertion (A)
The number of coins of diameter 1.75 cm and 2 mm thickness that can be formed 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 =(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.

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Solution

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Assertion (A):
Volume of the cuboid =l×b×h
=10×5.5×3.5 cm3
Volume of each coin=πr2h
=227×175200×175200×15 d=1.75cmr=1.752cm, h=2mmh=210cm

Number of coins=Volume of the cuboidVolume of each coin

=10×55×35×7×200×200×510×10×22×175×175=400
Hence, Assertion (A) is true.

Reason (R): The given statement is true.

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