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Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5(sqrt 3)cm is 500 pi cm^3

Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5(sqrt 3)cm is 500 pi cm^3

Grade:12

3 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago

putting the values give maximum volume of the cylinder which can be inscribed in a sphere of radius 5(sqrt 3)cm is 500 pi cm^3
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hi

please evaluate yourself.

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty
Priya
11 Points
7 years ago
Draw a sphere inside the sphere draw a cylinder .Draw a line through the centre if the cylinder (diagonal)
If that length is AB then AB=2R
AC (diameter of the circlular portion if the cylinder)=2r and BC(height)=h.
AB2=AC2+BC2
4R2=4r2-h2/4
Volume = pi r2h
substitute for r2.
differentiate it.put dv/dh=0.
u get h=2R/root(3).
put that value in vol eq to get the required ans
hope u understood..!

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