On a rainy day, 60 cm of rain is recorded in a region. What is the volume of water collected in an open and empty rectangular water tank that measures 12 m (length) `xx 10 m` (width) and 50 cm (depth) ?

Options

A. `120 m^(3)`
B. `72 m^(3)`
C. `60 m^(3)`
D. `48 m^(3)`

Answer

To find the volume of water collected in the rectangular water tank during the rainy day, we need to follow these steps:

### Step 1: Convert all measurements to the same unit
The dimensions of the tank are given in meters and centimeters. To make calculations easier, we will convert the depth of the tank from centimeters to meters.

- Depth of the tank = 50 cm = 50/100 m = 0.5 m

### Step 2: Determine the effective height of water that can be collected
Since the rain recorded is 60 cm (or 0.6 m), but the tank can only hold up to 50 cm (or 0.5 m) before overflowing, we will use the height of the tank for our calculations.

- Effective height of water = 0.5 m (as the tank will overflow after this height)

### Step 3: Use the formula for the volume of a rectangular prism
The volume \( V \) of a rectangular tank is given by the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]

### Step 4: Substitute the values into the formula
- Length of the tank = 12 m
- Width of the tank = 10 m
- Height of the water = 0.5 m

Now, substituting these values into the formula:
\[ V = 12 \, \text{m} \times 10 \, \text{m} \times 0.5 \, \text{m} \]

### Step 5: Calculate the volume
\[ V = 12 \times 10 \times 0.5 = 60 \, \text{m}^3 \]

### Final Answer
The volume of water collected in the tank is **60 cubic meters (m³)**.

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