Two tanks are of the same capacity. The dimensions of the first tank are `12cmxx8cmxx4cm`. The second tank has a square base with depth 6 cm, then find the side of the square.

Options

A. 12 cm
B. 6 cm
C. 8 cm
D. 10 cm

Answer

To solve the problem step by step, we need to find the side length of the square base of the second tank, given that both tanks have the same capacity.

### Step 1: Calculate the volume of the first tank
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
For the first tank, the dimensions are:
- Length = 12 cm
- Breadth = 8 cm
- Height = 4 cm

Substituting the values:
\[ V_1 = 12 \, \text{cm} \times 8 \, \text{cm} \times 4 \, \text{cm} \]
\[ V_1 = 384 \, \text{cm}^3 \]

### Step 2: Set up the volume equation for the second tank
The second tank has a square base with side length \( x \) and a height of 6 cm. The volume \( V \) of the second tank can be calculated as:
\[ V_2 = \text{side}^2 \times \text{height} = x^2 \times 6 \]

### Step 3: Set the volumes equal to each other
Since both tanks have the same capacity, we can set their volumes equal:
\[ V_1 = V_2 \]
\[ 384 \, \text{cm}^3 = x^2 \times 6 \]

### Step 4: Solve for \( x^2 \)
To find \( x^2 \), we can rearrange the equation:
\[ x^2 = \frac{384}{6} \]
Calculating the right side:
\[ x^2 = 64 \]

### Step 5: Calculate \( x \)
To find \( x \), we take the square root of both sides:
\[ x = \sqrt{64} \]
\[ x = 8 \, \text{cm} \]

### Conclusion
The side length of the square base of the second tank is \( 8 \, \text{cm} \).

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