A water tank is 11 m long, 10 m wide and 9 m high. It is filled with water to a level of 6 m. What part of the tank is empty?

Options

A. `1/4th`
B. `1/3rd`
C. `1/6th`
D. `2/3rd`

Answer

To solve the problem step by step, we will calculate the volume of the tank, the volume of the water filled, and then determine the empty volume and its fraction of the total tank volume.

### Step 1: Calculate the volume of the tank
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = 11 m
- Width = 10 m
- Height = 9 m

Substituting the values:
\[ V = 11 \, \text{m} \times 10 \, \text{m} \times 9 \, \text{m} = 990 \, \text{m}^3 \]

### Step 2: Calculate the volume of water filled in the tank
The volume of water filled up to a height of 6 m can be calculated using the same formula:
\[ V_{\text{filled}} = \text{length} \times \text{width} \times \text{height filled} \]
Given:
- Height filled = 6 m

Substituting the values:
\[ V_{\text{filled}} = 11 \, \text{m} \times 10 \, \text{m} \times 6 \, \text{m} = 660 \, \text{m}^3 \]

### Step 3: Calculate the empty volume of the tank
The empty volume of the tank can be found by subtracting the volume of water filled from the total volume of the tank:
\[ V_{\text{empty}} = V - V_{\text{filled}} \]
Substituting the values:
\[ V_{\text{empty}} = 990 \, \text{m}^3 - 660 \, \text{m}^3 = 330 \, \text{m}^3 \]

### Step 4: Calculate the fraction of the tank that is empty
To find the fraction of the tank that is empty, we divide the empty volume by the total volume of the tank:
\[ \text{Fraction empty} = \frac{V_{\text{empty}}}{V} \]
Substituting the values:
\[ \text{Fraction empty} = \frac{330 \, \text{m}^3}{990 \, \text{m}^3} = \frac{1}{3} \]

### Final Answer
Thus, the fraction of the tank that is empty is \( \frac{1}{3} \).

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