a solid sphere of radius 7 cm is melted to form cones and cylinder the requirement is such that no. of cones is twice the no. of cylinders and also radius of cone is equal to its height which should be equal to the radius of the cylinder and also height of one such cylinder is 4 cm find the maximum no. of cones which can be made out of sphere

Volume of Sphere = Total volume of cones + Total volume of Cylinders
Let the number of cylinders be 'n' , so the number of cones will be 2n
4/3 Pi r^3 = 2n*1/3 pi r^2h + n*pi r^2 *h
Also given that for cone the radius and height are same, which is also equal to the radius of cylinder. Height of Cylinder is 4 cm
So we have, 4/3 Pi 7^3 = 2n*1/3 pi r^3 + n*pi r^2 *4
=> 4/3*7^3 = 2n* r^2 (r/3 + 2)
=> n = ( 2)*7^3/(r^2(r+6))
Now for number of cones to be maximum, n should be maximum. Now for n to be maximum, r^3+6r^2 should be minimum. See if you could figure it out now.