Assertion (A) If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm,

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

$\pi\left\{R^{2}+r^{2}+l(R-r)\right\}$, 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.

 

Solution:

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.

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