Assertion : If the areas of three adjacent faces of a cuboid are x, y, z respectively then the volume of the cuboid is `sqrt(xyz).
Reason : Volume of a cuboid whose edges are l, b and h is lbh units.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the given problem, we need to analyze the assertion and reason provided regarding the volume of a cuboid based on the areas of its adjacent faces. Let's break it down step by step.

### Step 1: Understand the dimensions of the cuboid
Let the dimensions of the cuboid be:
- Length = \( l \)
- Breadth = \( b \)
- Height = \( h \)

### Step 2: Relate the areas of the adjacent faces to the dimensions
The areas of the three adjacent faces of the cuboid can be expressed as:
- Area of face 1 (length and breadth) = \( A_1 = l \times b = x \)
- Area of face 2 (breadth and height) = \( A_2 = b \times h = y \)
- Area of face 3 (height and length) = \( A_3 = h \times l = z \)

### Step 3: Write the equations based on the areas
From the above definitions, we can write:
1. \( l \times b = x \) (1)
2. \( b \times h = y \) (2)
3. \( h \times l = z \) (3)

### Step 4: Multiply the three equations
To find the volume, we can multiply all three equations:
\[ (x)(y)(z) = (l \times b)(b \times h)(h \times l) \]
This simplifies to:
\[ xyz = l^2 \times b^2 \times h^2 \]

### Step 5: Take the square root
Taking the square root of both sides gives us:
\[ \sqrt{xyz} = l \times b \times h \]
Here, \( l \times b \times h \) is the volume \( V \) of the cuboid.

### Step 6: Conclusion
Thus, we can conclude that:
\[ V = \sqrt{xyz} \]
This confirms the assertion that if the areas of three adjacent faces of a cuboid are \( x, y, z \) respectively, then the volume of the cuboid is \( \sqrt{xyz} \).

### Step 7: Evaluate the reason
The reason states that the volume of a cuboid whose edges are \( l, b, h \) is \( lbh \). This is also true as it is the standard formula for the volume of a cuboid.

### Final Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

---