Question

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 545π cm2.	If the radii of the circular ends of the frustum of a cone are R and r respectively and its height is h, π{R2 + r2 + l(R – r)}, where l2 = h2 + (R + r)2.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

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

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

Answer 1

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

Explanation:

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 cm

Surface area of the bucket = π[R² + r² + l(R + r)]

`= pixx[(15)^2 + (5)^2+26xx(15+5)]`

= π × [225 + 25 + 520]

= 770π cm² 

Thus, the area and the formula are wrong.