Find volume of a cuboid whose edges are `58.73cm,2.631 cm and 0.3798cm` using log table.

Answer

To find the volume of a cuboid with edges \(58.73 \, \text{cm}\), \(2.631 \, \text{cm}\), and \(0.3798 \, \text{cm}\) using logarithms, we can follow these steps:

### Step 1: Understand the formula for the volume of a cuboid
The volume \(V\) of a cuboid is given by the formula:
\[ V = A \times B \times C \]
where \(A\), \(B\), and \(C\) are the lengths of the edges.

### Step 2: Take the logarithm of both sides
Taking the logarithm (base 10) of both sides, we have:
\[ \log V = \log (A \times B \times C) \]
Using the property of logarithms that states \(\log (x \times y) = \log x + \log y\), we can rewrite this as:
\[ \log V = \log A + \log B + \log C \]

### Step 3: Substitute the values of the edges
Now we substitute the values of the edges into the equation:
\[ \log V = \log (58.73) + \log (2.631) + \log (0.3798) \]

### Step 4: Find the logarithms using a log table
Using a logarithm table, we find:
- \(\log (58.73) \approx 1.7688\)
- \(\log (2.631) \approx 0.4201\)
- \(\log (0.3798) \approx -0.4204\)

### Step 5: Add the logarithmic values
Now, we add these logarithmic values together:
\[ \log V = 1.7688 + 0.4201 - 0.4204 \]
Calculating this gives:
\[ \log V = 1.7688 + 0.4201 - 0.4204 = 1.7685 \]

### Step 6: Find the antilogarithm
To find \(V\), we need to calculate the antilogarithm of \(1.7685\):
\[ V = 10^{1.7685} \]

### Step 7: Calculate the antilogarithm using the log table
1. The integer part is \(1\), so we consider \(0.7685\).
2. Look up \(0.76\) in the log table, which gives a value of \(5.861\) in the 8th column.
3. The mean difference for the 5th column is \(7\), so we add \(7\) to \(5861\):
\[ 5861 + 7 = 5868 \]
4. Since the integer part of the logarithm is \(1\), we place the decimal after the first digit:
\[ V \approx 58.68 \, \text{cm}^3 \]

### Final Answer
The volume of the cuboid is approximately:
\[ \boxed{58.68 \, \text{cm}^3} \]