Chapter 6: Application of Derivatives

Let’s assume x be to the edge and r be the radius of the sphere.

Surface area of cube = 6x²

And, surface area of the sphere = 4πr²

Now, their sum is

Now,

So, it is the minima.

Therefore, the required ratio is 1: 1 when the combined volume is minimum.

Let consider AB be the diameter and C is any point on the circle with radius r.

∠ACB = 90^o [angle in the semi-circle is 90^o]

Let AC = x

Squaring on both the sides, we get

Therefore, the area of Δ ABC is minimum when it is an isosceles triangle.