Q. 764.0( 2 Votes )

# 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 cm^{2}.

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 {R^{2} + r^{2} + l(R - r)},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 :

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(r_{1} + r_{2}) + πr_{1}^{2} + πr_{2}^{2} (here l , r_{1}, r_{2} are the slant height, radii of the frustum)

Let S be the TSA of the bucket

∴ S = πl(r_{1} + r_{2}) + π(r_{2})^{2} (here , top of the bucket is not closed but bottom is closed, ∴ π(r_{2})^{2} = 0 )

l = √(h^{2} + (R-r)^{2})

⇒ S = π × √(h^{2} + (R-r)^{2}) × (r_{1} + r_{2}) + π(r_{2})^{2}

⇒ S = π × √(24^{2} + (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 cm^{2}

∴ The surface area of the bucket is 1711.3 cm^{2}

Reason(R):

Here,

Surface area is π {R^{2} + r^{2} + l(R + r)},where l^{2} = h^{2} + (R –r)^{2}.

Assertion is wrong and Reason is Wrong.

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