SOLUTION: There is a rectangular cuboid of dimention x , 2x and x/3 units and a sphere of radius " r ". The sum of their surface areas is constant.Prove that the sum of their volumes will b

Algebra ->  Geometry-proofs -> SOLUTION: There is a rectangular cuboid of dimention x , 2x and x/3 units and a sphere of radius " r ". The sum of their surface areas is constant.Prove that the sum of their volumes will b      Log On


   

Question 891065: There is a rectangular cuboid of dimention x , 2x and x/3 units and a sphere of radius " r ". The sum of their surface areas is constant.Prove that the sum of their volumes will be minimum if " x " is equal to three times the radius ( i.e. 3r ) of the sphere.

Please send me step by step full solution af the same.

regards,

Khoka123.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There is a rectangular cuboid of dimention x , 2x and x/3 units and a sphere of radius " r ". The sum of their surface areas is constant.Prove that the sum of their volumes will be minimum if " x " is equal to three times the radius ( i.e. 3r ) of the sphere.
----
Cuboid surface area = 2(x*2x + x*(x/3) + (2x)(x/3)) = 2(2x^2+(1/3)x^2+(2/3)x^2)
= 2(3x^2)
= 6x^2
------
Sphere surface area = 4pir^2
-----
Sum = 6x^2 + 4pir
-------
Comment:: This does not lead to the predicted solution.
Did you post the problem correctly?
---------------------
Cheers,
Stan H.
===================