The sides of a-cuboid are a, b, c. Its volume is V cu unit and total surface area be'S sq unit. Then, `1/V` = ?

Options

A. `1/2 S(a + b + c)`
B. `2/S (1/a + 1/b + 1/c)`
C. `(2S)/(a + b + c)`
D. `2S (a + b + c)`

Answer

To solve the problem, we need to find the value of \( \frac{1}{V} \) where \( V \) is the volume of a cuboid with sides \( a \), \( b \), and \( c \).

### Step-by-Step Solution:

1. **Understand the formulas**:
- The volume \( V \) of a cuboid is given by the formula:
\[ V = a \times b \times c \]
- The total surface area \( S \) of a cuboid is given by the formula:
\[ S = 2(ab + bc + ca) \]

2. **Express \( \frac{1}{V} \)**:
- We can express \( \frac{1}{V} \) in terms of \( S \):
\[ \frac{1}{V} = \frac{1}{abc} \]

3. **Relate \( S \) to \( V \)**:
- From the surface area formula, we can express \( S \) as:
\[ S = 2(ab + bc + ca) \]
- We can rewrite \( \frac{1}{V} \) using \( S \):
\[ \frac{1}{V} = \frac{2}{S} \cdot \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \]

4. **Final expression**:
- Therefore, we can conclude that:
\[ \frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \]

### Conclusion:
The final expression for \( \frac{1}{V} \) is:
\[ \frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right) \]