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 $=\left(\mathrm{\pi }{r}^{2}h\right)$ 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.

Answer 1

(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 $=\left(l\times b\times h\right)$
$=\left(10\times 5.5\times 3.5\right){\text{cm}}^3$
Volume of each coin$=\mathrm{\pi }{r}^{2}h$
$=\frac{22}{7}\times \frac{175}{200}\times \frac{175}{200}\times \frac{1}{5}\left[d=1.75\text{cm}\Rightarrow r=\frac{1.75}{2}\text{cm},h=2\text{mm}\Rightarrow h=\frac{2}{10}\text{cm}\right]$

Number of coins$=\frac{\text{Volume of the cuboid}}{\text{Volume of each coin}}$

$$\begin{gathered} =\frac{10\times 55\times 35\times 7\times 200\times 200\times 5}{10\times 10\times 22\times 175\times 175} \\ =400 \end{gathered}$$
Hence, Assertion (A) is true.

Reason (R): The given statement is true.