The areas of three adjacent faces of a cuboid are a `m^2`,b `m^2` and c `m^2` respectively. Twice of its volume is

Options

A. `"2abc m"^3`
B. `2sqrt(a^2+b^2+c^2) m^3`
C. `2sqrt(abc) m^3`
D. `6sqrt(abc) m^3`

Answer

To find twice the volume of a cuboid given the areas of its three adjacent faces, we can follow these steps:

### Step 1: Understand the given areas
Let the areas of the three adjacent faces of the cuboid be:
- Area of face 1 (length × breadth) = A m²
- Area of face 2 (breadth × height) = B m²
- Area of face 3 (length × height) = C m²

### Step 2: Set up equations for dimensions
From the areas, we can set up the following equations:
1. \( L \times B = A \) (1)
2. \( B \times H = B \) (2)
3. \( L \times H = C \) (3)

### Step 3: Express the volume
The volume \( V \) of the cuboid is given by:
\[ V = L \times B \times H \]

### Step 4: Multiply the equations
To find \( V \), we can multiply equations (1), (2), and (3):
\[ (L \times B) \times (B \times H) \times (L \times H) = A \times B \times C \]
This simplifies to:
\[ L^2 \times B^2 \times H^2 = A \times B \times C \]

### Step 5: Take the square root
Taking the square root of both sides gives:
\[ L \times B \times H = \sqrt{A \times B \times C} \]
Thus, the volume \( V \) can be expressed as:
\[ V = \sqrt{A \times B \times C} \]

### Step 6: Calculate twice the volume
To find twice the volume, we multiply by 2:
\[ 2V = 2 \times \sqrt{A \times B \times C} \]

### Final Answer
Thus, the final expression for twice the volume of the cuboid is:
\[ \text{Twice the volume} = 2 \sqrt{A \times B \times C} \text{ m}^3 \]

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