Question

Assertion: From a rectangular sheet 40 cm by 28 cm, a square with side 5 cm is cut off from each of its corners. The volume of the open box formed with the remaining sheet is 2700 cm³.

Reason: Longest diagonal of a cuboid is `sqrt(l^2 + b^2 + h^2)`

विकल्प

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

Assertion (A):

We are given a rectangular sheet with dimensions 40 cm × 28 cm and squares of side 5 cm are cut off from each corner. We are asked to find the volume of the open box formed from the remaining sheet, which is said to be 2700 cm³.

To form the open box:

• The length of the box is 40 − 2 × 5 = 30 cm (since 5 cm is cut off from both ends of the length).
• The width of the box is 28 − 2 × 5 = 18 cm (since 5 cm is cut off from both ends of the width).
• The height of the box is the side of the square cut off, which is 5 cm.

Now, the volume V of the open box is given by:

V = length × width × height

Substitute the values:

V = 30 × 18 × 5 = 2700 cm³

Thus, the Assertion is true because the volume of the open box is indeed 2700 cm³.

Reason (R):

The longest diagonal of a cuboid (box) is given by the formula:

`d = sqrt(l^2 + b^2 + h^2)`

where l is the length, b is the breadth and h is the height of the cuboid. This is the correct formula for finding the longest diagonal of a cuboid.

Thus, the Reason is true.