Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
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 545 π 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 π {R2 + r2 + l(R - r)},where l2 = h2 + (R –r)2.
Assertion is wrong and Reason is Wrong.
Explanation:
Assertion (A):
Given: The radii of the end of a bucket are 5 cm and 15 cm and it is 24 cm high
Bucket is in the shape of frustum.
TSA of a frustum of a cone = πl(r1 + r2) + πr12 + πr22 (here l , r1, r2 are the slant height, radii of the frustum)
Let S be the TSA of the bucket
∴ S = πl(r1 + r2) + π(r2)2 (here , top of the bucket is not closed but bottom is closed, ∴ π(r2)2 = 0 )
l = √(h2 + (R-r)2)
⇒ S = π × √(h2 + (R-r)2) × (r1 + r2) + π(r2)2
⇒ S = π × √(242 + (15-5)2) × (5 + 15) + π × (5)2
⇒ S = π × √(576 + 100) × (20) + π × 25
⇒ S = π × √(676) × (20) + π × 25
⇒ S = π × 26 × (20) + π × 25
⇒ S = π × 520 + π × 25
⇒ S = π × (520 + 25)
⇒ S= 3.14 × 545 = 1711.3 cm2
∴ The surface area of the bucket is 1711.3 cm2
Reason(R):
Here,
Surface area is π {R2 + r2 + l(R + r)},where l2 = h2 + (R –r)2.
Assertion is wrong and Reason is Wrong.