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 curved surface area of a cone of base radius $3\ cm$ and height $4\ cm$ is $ \ (15\pi\text{ cm}^2$ Volume of a cone $ (\pi\text{r}^2\text{h}$
  • 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 $(A).$
  • Assertion $(A)$ is true and Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false and Reason $(R)$ is true.

Answer

Correct option: C.
Assertion $(A)$ is true and Reason $(R)$ is false.
$\text{l}\sqrt{\text{r}^2+\text{h}^2}$
$\Rightarrow\text{l}=\sqrt{3^2+4^2}$
$\Rightarrow\text{l}=\sqrt{9+16}$
$\Rightarrow\text{l}=\sqrt{25}$
$\Rightarrow\text{l}=5\text{cm}$
Curved surface area of a cone
$=\pi\text{rl}$
$=\pi(3)(5)$
$=15\pi\text{ cm}^2$
So, the Assertion $(A)$ is true.
Volume of a cone $=\frac{1}{3}\pi\text{r}^2\text{h}$
So, the reason $(R)$ is false.

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