Show that the surface area of a closed cuboid with a square base and

given volume is minimum, when it is cube.

 

here what will be its volume

(1)x³ 

(2)x²h

Let x be side of the square base and h be the height of the cuboid

but why volume have taken 'x²h' 

can we take it as x³ as it told that its acube finally

 

Hi Rahul!

 

You have to show that the surface area of a closed cuboid with a square base and given volume is minimum when it is cube. Here, you are given with a cuboid (not a cube) whose base is a square. You need to show that the given cuboid is a cube i.e. the height of the cuboid = side of the square base of the cuboid i.e h = x.

 

That is why considering the side of the squared base of the cuboid as x and height h, the volume of the cuboid will be x²h.

 

Hope! This will help you.

 

Cheers!!!