MCQ
Assertion and Reason Type
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R)$. For selecting the correct answer, use the following code:
Assertion (A)
Reason (R)
The number of coins of $1.75\ cm$ in diameter and $2\ mm$ thick from a melted cuboid $(10\ cm \times 5.5\ cm \times 3.5\ cm)$ is $400.$
Volume of a cylinder of base radius $r$ and height $h$ is given by $\text{V}=(\pi\text{r}^2\text{h})$ cubic units. And volume of a cuboid $= (l \times b \times h)$ cubic units.
  • 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

Correct option: A.
Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
Volume of the cuboid $=(10\times5.5\times3.5)\text{cm}^3$
Volume of each cone $=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times\frac{1.75}{2}\times\frac{1.75}{2}\times\frac{1}{5}$
Number of cone $=\frac{\text{volume of the cuboid}}{\text{Volume of each coin}}$
$=\frac{10\times5.5\times3.5}{\frac{22}{7}\times\frac{1.75}{2}\times\frac{1.75}{2}\times\frac{1}{5}}$
$=400$
So, the Assertion $(A)$ is true.
The Reason $(R)$ is also true and is the correct explanation for the Assertion $(A).$

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