Question

Assertion (A)
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 545π cm².

Reason(R)
If the radii of the circular ends of the frustum of a cone are R and r, respectively, and its height is h, then its surface area is $\mathrm{\pi }\{R^2+r^2+l(R-r\left)\right\},\mathrm{where}{l}^2=h^2+(R-r{)}^2.$

(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.
(d) Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A):
Let R and r be the top and base of the bucket and let h be its height.
Then, R = 15 cm, r = 5 cm and h = 24 cm
Slant height, $l=\sqrt{h^2+{\left(R-r\right)}^2}$
$$\begin{gathered} =\sqrt{{\left(24\right)}^2+{\left(15-5\right)}^2} \\ =\sqrt{576+100} \\ =\sqrt{676} \\ =26\text{cm} \end{gathered}$$
Surface area of the bucket$=\mathrm{\pi }\left[R^2+r^2+l\left(R+r\right)\right]$
$$\begin{gathered} =\mathrm{\pi }\times \left[{\left(15\right)}^2+{\left(5\right)}^2+26\times \left(15+5\right)\right] \\ =\mathrm{\pi }\times \left[225+25+520\right] \\ =770\mathrm{\pi }{\mathrm{cm}}^2 \end{gathered}$$
Thus, the area and the formula are wrong.

Note:
Question seems to be incorrect.