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 $(R)$
If the radii of the circular ends of a bucket $24\ cm$ high are $15\ cm$ and $5\ cm$ respectively, then the surface area of the bucket is $545\pi\text{cm}^2.$
if the radii of the circular ends of the frustum of a cone are $R$ and $r$ respectively and its height is $h,$ surface area is:
$\pi\big\{\text{R}^2+\text{r}^2+\text{l}(\text{R}-\text{r})\big\}$
where $\text{l}^2=\text{h}^2+(\text{R}+\text{r})^2.$
  • 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.
  • Assertion $(A)$ is false and Reason $(R)$ is true.

Answer

Correct option: D.
Assertion $(A)$ is false and Reason $(R)$ is true.
Slant height $=\sqrt{\text{h}^2+(\text{R}-\text{r})^2}$
$=\sqrt{24^2+(15-5)^2}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26\text{cm}$
Surface area of the bucket $=\big[\text{R}^2+\text{r}^2+\text{l}(\text{R}+\text{r})\big]$
$=\pi\big[15^2+5^2+26(15+5)\big]$
$=\pi\big[225+25+520\big]$
$=770\pi\text{cm}^2$

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