Question
The sum of the surface areas of a cuboid with sides and and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if is equal to three times the radius of sphere. Also find the minimum value of the sum of their volumes.
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Practice questions from similar books
Question 1
A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the parabola at the point art . The tangent to the parabola at intersects the y-axis at . The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum P) m= Q) = Maximum area of is (R) (S) Question 2
Show that a right-circular cylinder of given volume, open at the top, has minimum total surface area, provided its height is equal to the radius of the base.Question Text | The sum of the surface areas of a cuboid with sides and and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if is equal to three times the radius of sphere. Also find the minimum value of the sum of their volumes. |