CBSE Class 12 Math 2022 Term I Solved Paper

Section C

Attempt any 8 questions out of the Questions 41-50. Each question is of one mark.

Question : 41

Total: 50

In a sphere of radius r, a right circular cone of height h having maximum curved surface area is inscribed. The expression for the square of curved surface of cone is

2π2rh(2rh+h2)
π2hr(2rh+h2)
2π2r(2rh2−h3)
2π2r2(2rh−h2)

Solution: 👈: Video Solution

Here, ‌‌ CSA of cone =πRl
Radius of sphere =r
height of cone =h
In △AOC ,
AO2=AC2+OC2
⇒‌‌r2=R2+(h−r)2
⇒‌‌R2=2hr−h2
∴‌‌ Radius of cone, R=√2hr−h2‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
In △ABC ,
AB2‌=AC2+BC2
⇒l2‌=R2+h2
⇒l2‌=2hr−h2+h2
∴ slant height ‌‌=√2hr‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
CSA of cone =πRl
‌=π√2hr−h2√2hr
(‌ CSA of cone ‌)2‌=π2(2hr−h2)(2hr)
‌=2π2hr(2hr−h2)
‌=2π2r(2rh2−h3)

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