Question

Prove that all rectangular parallelopipe with same volume, the cube has the least surface

Answer 1

Answer:

$.$

Step-by-step explanation:

Length: Breadth: Height::6:3:1

Let the height of the parallelopiped be x.

Thus Length and Breadth are6x and 3x.

Surface area of parallelopiped is 2$$(LB+LH+HB)=2(6x×3x+6x×x+3x×x)=54x^2.$$

Surface area of cube is 6h

2

Thus 6h

2

=54x

2

.

h

2

=9x

2

h=3x

Now ratio of volume

volume of parallelopiped

volume of cube = 3x 55