Answer:
Step-by-step explanation:
given,
radius of sphere = 3
volume of cone:
r is the radius of circular base
h is the height of the cone
here r = x and h = 3 + y
now, volume in term of x and y
Applying Pythagoras theorem
x² + y² = 3²
differentiating both side
for maxima
y² + 2 y - 3 = 0
(y+3)(y-1)=0
y = 1,-3
y cannot be negative so, volume at y = 1
Hence, the largest cone which can be inscribed in the spheres of the radius 3 has volume