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Mathematics

Assertion (A) : The length, breadth and height of an open cuboid are 10 cm, 12 cm and 6 cm respectively. If the thickness is 1 cm, then internal dimensions are 8 cm, 10 cm and 5 cm respectively.

Reason (R) : If l, b and h are the external dimension of an open cuboid of thickness 'x', then its internal dimension are (l - 2x), (b - 2x) and (h - x) respectively.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Surface Area, Volume, Capacity

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Answer

l, b and h represent the external length, breadth, and height, respectively.

The wall has thickness 'x'.

The internal dimensions are reduced by the thickness of the walls.

The internal length = (l - 2x), accounting for the thickness on both sides.

The internal breadth = (b - 2x), accounting for the thickness on both sides.

The internal height = (h - x), as the thickness affects only the bottom and sides, not the open top.

So, reason (R) is true.

10 cm, 12 cm and 6 cm are the external length, breadth, and height, respectively.

The wall has thickness 1 cm.

The internal length = (10 - 2 x 1) = (10 - 2) = 8 cm.

The internal breadth = (12 - 2 x 1) = (12 - 2) = 10 cm.

The internal height = (6 - 1) = 5 cm.

So, assertion (A) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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