Question
The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is
BITSAT
Mathematics
Application of Derivatives
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 384 3
- B. 768 3
- C. 768 3
- D. 1152 3
Answer
B. 768 3
Step-by-step solution
12^2=r^2+ ( h 2 )^2 V= r^2 h V= (144- h^2 4 ) h V=144 h- 4 h^3 d V d h =144 - 3 4 h^2 d V d h =0 144 = 3 4 h^2 h^2=48 4 h=8 3 12^2=r^2+48 r^2=96 Volume = r^2 h= 96 8 3 =768 3 ~cm ^3.
Related: Mathematics — Application of Derivatives · All PYQ Banks