A rectangular tank 25 cm long and 20 cm wide contains `4.5` litres of water. When a metal cube is low ered in the tank, the water level rises to a height of 11 cm. Find the length of each edge of the cube ?

Options

A. 15 cm
B. 5 cm
C. 11 cm
D. 10 cm

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the dimensions of the tank
The tank is given as:
- Length = 25 cm
- Width = 20 cm

### Step 2: Convert the volume of water from liters to cubic centimeters
We know that:
1 liter = 1000 cubic centimeters (cm³)
Thus, the volume of water in the tank is:
\[ 4.5 \text{ liters} = 4.5 \times 1000 = 4500 \text{ cm}^3 \]

### Step 3: Calculate the area of the base of the tank
The area of the base (A) of the rectangular tank can be calculated as:
\[ A = \text{Length} \times \text{Width} = 25 \text{ cm} \times 20 \text{ cm} = 500 \text{ cm}^2 \]

### Step 4: Calculate the initial height of the water
Using the formula for volume:
\[ \text{Volume} = \text{Area of base} \times \text{Height} \]
We can rearrange this to find the height (h):
\[ h = \frac{\text{Volume}}{\text{Area of base}} = \frac{4500 \text{ cm}^3}{500 \text{ cm}^2} = 9 \text{ cm} \]

### Step 5: Determine the rise in water level after adding the cube
The new height of the water after the cube is added is given as 11 cm. Therefore, the rise in water level is:
\[ \text{Rise in height} = 11 \text{ cm} - 9 \text{ cm} = 2 \text{ cm} \]

### Step 6: Calculate the volume of water displaced by the cube
The volume of water displaced (which is equal to the volume of the cube) can be calculated as:
\[ \text{Volume of water displaced} = \text{Area of base} \times \text{Rise in height} \]
\[ = 500 \text{ cm}^2 \times 2 \text{ cm} = 1000 \text{ cm}^3 \]

### Step 7: Relate the volume of the cube to its edge length
The volume (V) of a cube with edge length \( a \) is given by:
\[ V = a^3 \]
Setting this equal to the volume of the water displaced:
\[ a^3 = 1000 \text{ cm}^3 \]

### Step 8: Solve for the edge length of the cube
Taking the cube root of both sides:
\[ a = \sqrt[3]{1000} = 10 \text{ cm} \]

### Conclusion
The length of each edge of the cube is:
\[ \text{Edge length} = 10 \text{ cm} \]

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