Which of the following statements is/are true A: If the length of a cuboid is ‘x’ and its breadth and height are respectively (1/2) and (1/3) of its length, then the ratio of its surface is and its volume will be 12: x. B: If main diagonal of a cube becomes half, then the side of cube will also become half. C: If breadth of a cuboid is half of its length and it is cut into two equal pieces along the axes perpendicular to its length, then the 2 pieces formed will be cubes.?

Option 3 : Only A and B

CONCEPT:

Properties of cube and cuboid.

FORMULA USED:

Volume of cuboid = lbh

CALCULATION:

A: Since, length of the cuboid is ‘x’

Its breadth and height will be (x/2) and (x/3) respectively.

Now its volume will be x × (x/2) × (x/3) = x³/6 and

Its surface area will be 2 = 2x²

So, ratio between its surface are and volume is 2x²: x³/6 = 12: x.

B: Let the side of a cube is ‘a’

We know that, diagonal of the cube is ‘a√3’.

When the diagonal becomes half, then its diagonal will be ‘a√3/2’ and its side will be ‘a/2’.

C: In a cuboid the breadth is half of its length.

When it is cut into two equal pieces along the axes perpendicular to its length, the length and breadth of pieces will be equal.

In a cube: length, breadth and height should be equal, but there is no information about the height.