Question

Assertion: The dimensions of a cuboid are x, y and z. If xy = 20, yz = 10 and xz = 18, the volume of the cuboid is 60 cubic units.

Reason: The volume of a cuboid = length × breadth × height.

Options

• 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 and R is the correct reason for A.

Explanation:

Assertion (A):

We are given the dimensions of a cuboid as xxx, yyy, and zzz, with the following relationships:

• xy = 20
• yz = 10
• xz = 18

We are asked to check if the volume of the cuboid is 60 cubic units.

To find the volume of the cuboid, we use the formula for the volume of a cuboid:

V = x × y × z

To find x × y × z, we can multiply the three given equations:

(xy)(yz)(xz) = (x × y × z)²

Substitute the given values:

20 × 10 × 18 = (x × y × z)²

3600 = (x × y × z)²

Now, take the square root of both sides:

`x xx y xx z = sqrt(3600) = 60`

Thus, the volume of the cuboid is indeed 60 cubic units, so the Assertion is true.

Reason (R):

The volume of a cuboid is given by the formula:

V = length × breadth × height

This is the correct formula for the volume of a cuboid, so the Reason is true.