Q. 233.7( 34 Votes )
Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is 
of the volume of the sphere.
Answer :
Let r and h be the radius and height of the cone respectively inscribed in a sphere of radius R.
Let V be the volume of cone.
Then, V= 
And height of cone h = R + 
Now, 
Now, if, 
After solving this we get, 
So, when, 
, then 
< 0
Then, by second derivative test, the volume of the cone is the maximum when 
So, when, 
, h = R +
Therefore, V = 
Therefore, the volume of the largest cone that can be inscribed in the sphere is 
the volume of the sphere.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
PREVIOUSA wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?NEXTShow that the right circular cone of least curved surface and given volume has an altitude equal to √2 time the radius of the base.
RELATED QUESTIONS :
Show that the maximum value of 
is 
Mark (√) against the correct answer in the following:
At 
is
RS Aggarwal - Mathematics
Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:
RS Aggarwal - Mathematics
Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:
RS Aggarwal - Mathematics
