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Class 12 Applications Of Derivatives · Mcq Single Correct1 Marksoptimization

Class 12 Maths · Applications Of Derivatives · Mcq Single Correct #12

A right circular cone of height h is inscribed in a sphere of radius r, with 0<h<2r. Which expression equals the square of its curved surface area?
Cone inscribed in sphere: axial section
Cone inscribed in sphere: axial section

✅ Step-by-Step Solution

Final Answer: Option (C): 2π²r(2rh²−h³)
  1. The base radius ρ satisfies ρ²=r²−(h−r)²=2rh−h², and slant height l satisfies l²=ρ²+h²=2rh. Thus (πρl)²=2π²r(2rh²−h³).

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