A water tank is 13 m long, 14 m wide and 10 m deep. It is filled with water to a level of 5 m, what part of the tank is empty?

Options

A. `(1)/(2)`
B. `(3)/(2)`
C. `(2)/(3)`
D. `(1)/(3)`

Answer

To find out what part of the water tank is empty, we can follow these steps:

### Step 1: Calculate the total volume of the tank
The volume of a rectangular tank can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Given:
- Length = 13 m
- Width = 14 m
- Height = 10 m

Substituting the values:
\[ \text{Total Volume} = 13 \, \text{m} \times 14 \, \text{m} \times 10 \, \text{m} = 1820 \, \text{m}^3 \]

### Step 2: Calculate the volume of water in the tank
The tank is filled to a level of 5 m. We can calculate the volume of water in the tank using the same formula:
\[ \text{Volume of Water} = \text{Length} \times \text{Width} \times \text{Height of Water} \]
Where the height of water is 5 m:
\[ \text{Volume of Water} = 13 \, \text{m} \times 14 \, \text{m} \times 5 \, \text{m} = 910 \, \text{m}^3 \]

### Step 3: Calculate the volume of the empty part of the tank
To find the volume of the empty part of the tank, we subtract the volume of water from the total volume of the tank:
\[ \text{Volume of Empty Part} = \text{Total Volume} - \text{Volume of Water} \]
Substituting the values:
\[ \text{Volume of Empty Part} = 1820 \, \text{m}^3 - 910 \, \text{m}^3 = 910 \, \text{m}^3 \]

### Step 4: Determine the part of the tank that is empty
To find the part of the tank that is empty, we can express the empty volume as a fraction of the total volume:
\[ \text{Part of Tank Empty} = \frac{\text{Volume of Empty Part}}{\text{Total Volume}} = \frac{910 \, \text{m}^3}{1820 \, \text{m}^3} = \frac{1}{2} \]

### Final Answer
The part of the tank that is empty is \( \frac{1}{2} \) or half of the tank.

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