Question

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

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

The Reason (R) is clearly true.

Radius of each coin = `(1.75)/2` cm, thickness = `2/10` cm = `1/5` cm.

∴ Volume of each coin = πr²h 

= `(22/7 xx 1.75/2 xx 1.75/2 xx 1/5) cm^3`

= `(11/70 xx 175/100 xx 175/100) cm^3`

= `77/160 cm^3`

Volume of cuboid = `(10 xx 55/10 xx 35/10) cm^3`

= `385/2 cm^3`

Number of coins = `(385/2 xx 160/77)`

= 400, which is true.

Clearly, Reason (R) is true and Assertion (A) gives Reason (R).