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
$\pi\left\{R^{2}+r^{2}+l(R-r)\right\}$, 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.
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, $l=\sqrt{h^{2}+(R-r)^{2}}$
$=\sqrt{(24)^{2}+(15-5)^{2}}$
$=\sqrt{576+100}$
$=\sqrt{676}$
$=26 \mathrm{~cm}$
Surface area of the bucket $=\pi\left[R^{2}+r^{2}+l(R+r)\right]$
$=\pi \times\left[(15)^{2}+(5)^{2}+26 \times(15+5)\right]$
$=\pi \times[225+25+520]$
$=770 \pi \mathrm{cm}^{2}$
Thus, the area and the formula are wrong.
Note:
Question seems to be incorrect.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.