AP EAMCET · Maths · Application of Derivatives

If the curved surface area of right circular cylinder inscribed in a sphere of radius $22 cm$ is maximum then height of the cylinder will be

A $\frac{11}{\sqrt{2}} cm$
B $11 \sqrt{2} cm$
C $(0.22) \sqrt{2} m$
D $(0.11) \sqrt{2} m$

Verified Solution

Answer & Solution

Correct Answer

(B) $11 \sqrt{2} cm$

Step-by-step Solution

Detailed explanation

Curved surface area=2πrh A=2πh(484-h2) r2+h2=(22)2 ⇒dAdh=2π484-h2+-2h22484-h2=0 ⇒484-h2-h2=0 ⇒h2=242 ⇒h=112 cm

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If the curved surface area of right circular cylinder inscribed in a sphere of radius 22 cm is maximum then height of the cylinder will be

Step-by-step Solution

If the curved surface area of right circular cylinder inscribed in a sphere of radius $22 cm$ is maximum then height of the cylinder will be