A rectangular tank 25 cm long and 20 cm wide contains water to a depth of 5 cm . A metal cube of side 10 cm is placed in the tank so that one face of the cube rests on the bottom of the tank . Find how many litres of water must be poured into the tank so as to just cover the cube ?

Options

A. 1 L
B. 1.5 L
C. 2L
D. 2.5 L

Answer

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

### Step 1: Calculate the volume of water currently in the tank.
The volume of water in the tank can be calculated using the formula for the volume of a rectangular prism:

\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

Given:
- Length = 25 cm
- Width = 20 cm
- Height of water = 5 cm

\[ \text{Volume of water} = 25 \, \text{cm} \times 20 \, \text{cm} \times 5 \, \text{cm} = 2500 \, \text{cm}^3 \]

### Step 2: Determine the height of water needed to cover the cube.
The side of the cube is 10 cm, and since one face of the cube is resting on the bottom of the tank, we need to cover the cube with water to a height of 10 cm. However, there is already 5 cm of water in the tank.

To find out how much more water is needed to cover the cube, we subtract the current water height from the height needed to cover the cube:

\[ \text{Additional height needed} = 10 \, \text{cm} - 5 \, \text{cm} = 5 \, \text{cm} \]

### Step 3: Calculate the volume of water needed to cover the additional height.
Now, we need to find the volume of water that corresponds to this additional height of 5 cm.

\[ \text{Volume of additional water} = \text{Length} \times \text{Width} \times \text{Additional height} \]

Using the dimensions of the tank:

\[ \text{Volume of additional water} = 25 \, \text{cm} \times 20 \, \text{cm} \times 5 \, \text{cm} = 2500 \, \text{cm}^3 \]

### Step 4: Convert the volume from cubic centimeters to liters.
We know that 1 liter is equal to 1000 cubic centimeters. Therefore, to convert cubic centimeters to liters, we divide by 1000:

\[ \text{Volume in liters} = \frac{2500 \, \text{cm}^3}{1000} = 2.5 \, \text{liters} \]

### Final Answer:
To just cover the cube, we need to pour **2.5 liters** of water into the tank.

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