The capacity of a rectangular tank is ` 5.2 cm ^(3) ` and the area of its base is ` 2.6 xx 10 ^(4) cm ^(2)` find its height (depth).

Answer

To find the height (depth) of the rectangular tank, we will use the formula for the volume of a cuboid, which is given by:

\[ \text{Volume} = \text{Base Area} \times \text{Height} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Volume (Capacity) of the tank, \( V = 5.2 \, \text{cm}^3 \)
- Area of the base, \( A = 2.6 \times 10^4 \, \text{cm}^2 \)

2. **Use the Volume Formula:**
- According to the formula, we can express the height \( h \) in terms of volume and area:
\[ V = A \times h \]
Rearranging this gives:
\[ h = \frac{V}{A} \]

3. **Substitute the Values:**
- Now, substitute the values of \( V \) and \( A \) into the equation:
\[ h = \frac{5.2 \, \text{cm}^3}{2.6 \times 10^4 \, \text{cm}^2} \]

4. **Calculate the Height:**
- Perform the division:
\[ h = \frac{5.2}{2.6 \times 10^4} \]
- First, calculate \( \frac{5.2}{2.6} \):
\[ \frac{5.2}{2.6} = 2 \]
- Now, substituting back:
\[ h = \frac{2}{10^4} \]
- This can be expressed as:
\[ h = 2 \times 10^{-4} \, \text{cm} \]
- Converting this to decimal form gives:
\[ h = 0.0002 \, \text{cm} \]

5. **Final Answer:**
- The height (depth) of the rectangular tank is:
\[ h = 0.0002 \, \text{cm} \]