A rectangular vessel is 10 cm long and 8 cm wide. How high it must be made to hold 480 cubic centimetres of liquid?

Answer

To find the height of the rectangular vessel that can hold 480 cubic centimeters of liquid, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the dimensions of the vessel:**
- Length (L) = 10 cm
- Width (B) = 8 cm
- Height (H) = ? (This is what we need to find)

2. **Use the formula for the volume of a rectangular prism:**
The volume (V) of a rectangular prism (or vessel) is given by the formula:
\[ V = L \times B \times H \]
We know the volume (V) is 480 cubic centimeters.

3. **Set up the equation using the known values:**
Substitute the known values into the volume formula:
\[ 480 = 10 \times 8 \times H \]

4. **Calculate the product of length and width:**
First, calculate \(10 \times 8\):
\[ 10 \times 8 = 80 \]
So, the equation now looks like:
\[ 480 = 80 \times H \]

5. **Solve for height (H):**
To find H, divide both sides of the equation by 80:
\[ H = \frac{480}{80} \]

6. **Perform the division:**
Calculate \(480 \div 80\):
\[ H = 6 \text{ cm} \]

### Final Answer:
The height of the rectangular vessel must be **6 cm** to hold 480 cubic centimeters of liquid.

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