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 24cm high are 15cm and 5cm 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 $=\big[\text{R}^2+\text{r}^2+\text{l}(\text{R}+\text{r})\big]$

$=\pi\big[15^2+5^2+26(15+5)\big]$

$=\pi\big[225+25+520\big]$

$=770\pi\text{cm}^2$

The Assertion (A) and the Reason (R) are incorrect.

Note: The answer given in the text is incorrect.

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