To work out the depth (height) of water in a cuboid, you need to know the volume of the water and the length and width of the cuboid base. You can calculate the depth by dividing the water's volume by the area of the cuboid's base (length multiplied by width).
Understanding the Formula
The fundamental principle behind calculating the depth comes from the formula for the volume of a cuboid:
Volume (V) = Length (l) × Width (w) × Height (h)
In this case, the "height" is the depth of the water. The "volume" is the volume of the water filling the cuboid up to a certain level.
So, if we know the volume of the water (V), the length (l), and the width (w), we can rearrange the formula to solve for the height (h), which represents the depth of the water:
h = V / (l × w)
Calculating Water Depth: Step-by-Step
Using the provided reference, we understand the core method:
Since we already have two dimensions (the length and the width), we simply divide the volume in cm3 by the product of the length and width to calculate the height of the water. This is derived from the formula of volume of a cuboid: l×w×h=Vc , where l= length, w= width, h= height, and Vc= Volume of cuboid.
Here's how to apply this in practice:
- Find the Volume of the Water (V): Determine the volume of the water currently in the cuboid. This might be given in the problem, or you might need to measure it if possible (though typically problems involving this calculation provide the volume). Ensure the units are consistent (e.g., cubic centimeters cm³, cubic meters m³).
- Measure the Length (l) and Width (w): Measure the internal length and width of the cuboid's base. Ensure these measurements are in the same units as the volume (e.g., if volume is in cm³, length and width should be in cm).
- Calculate the Area of the Base: Multiply the length by the width (l × w). This gives you the area of the cuboid's base.
- Divide Volume by Base Area: Divide the volume of the water (V) by the calculated base area (l × w). The result is the depth of the water (h).
Example Calculation
Let's say you have a cuboid tank with:
- Length (l) = 50 cm
- Width (w) = 30 cm
- Volume of water (V) = 45,000 cm³
To find the depth of the water:
- Calculate the base area: Base Area = l × w = 50 cm × 30 cm = 1500 cm²
- Calculate the depth: Depth (h) = V / Base Area = 45,000 cm³ / 1500 cm² = 30 cm
So, the depth of the water in this cuboid is 30 cm.
Why This Works
This method works because the volume of the water forms a smaller cuboid shape within the larger tank, with the same base dimensions (length and width) as the tank, but with a different height – the depth of the water. By rearranging the volume formula, we isolate the height variable, allowing us to solve for it when the volume, length, and width are known.
| Measurement Required | Symbol | Description |
|---|---|---|
| Volume of Water | V | The total volume of liquid inside the cuboid. |
| Length of Base | l | The measurement along one side of the base. |
| Width of Base | w | The measurement along the adjacent side. |
| Depth of Water | h | The height of the water level. |
In summary, calculating the depth of water in a cuboid is a straightforward application of the volume formula, requiring you to divide the water's volume by the area of the base.
