The volume of a tank 10cm long, 5cm wide, and 8cm high is 400 cubic centimeters (cm³). Understanding how to calculate volume is essential for various practical applications, from determining the capacity of containers to estimating material requirements.
Understanding Volume and Rectangular Prisms
Volume refers to the amount of three-dimensional space occupied by an object or substance. For a tank with straight sides and a rectangular base, like the one described, it is geometrically classified as a rectangular prism or cuboid. Its volume is straightforwardly calculated by multiplying its three dimensions: length, width, and height.
The fundamental formula for the volume of a rectangular prism is:
Volume (V) = Length × Width × Height
Key dimensions to consider are:
- Length (l): The longest side of the base.
- Width (w): The shorter side of the base.
- Height (h): The vertical distance from the base to the top.
For further reading on the concept of volume, you can refer to Wikipedia's article on Volume. To learn more about the geometry of a cuboid, visit Wikipedia's page on Cuboids.
Step-by-Step Calculation
Let's apply the volume formula to the given dimensions of the tank to find its exact capacity.
Given Dimensions:
| Dimension | Value | Unit |
|---|---|---|
| Length | 10 | cm |
| Width | 5 | cm |
| Height | 8 | cm |
Calculation Process:
- Identify Dimensions: The tank has a length of 10 cm, a width of 5 cm, and a height of 8 cm.
- Apply the Volume Formula:
Volume = Length × Width × Height
Volume = 10 cm × 5 cm × 8 cm - Perform Multiplication:
- First, multiply the length by the width: 10 cm × 5 cm = 50 cm². This gives you the area of the base.
- Next, multiply this base area by the height: 50 cm² × 8 cm = 400 cm³.
- Final Result: The volume of the tank is 400 cm³. This confirms that a cuboid with these specific dimensions precisely holds 400 cubic centimeters of space.
Practical Significance and Unit Conversion
Knowing the volume in cubic centimeters is valuable for many purposes. For instance, when dealing with liquids, it's often helpful to convert cubic centimeters into more commonly used units like milliliters or liters.
- Capacity: The calculated volume directly represents the tank's capacity, indicating how much liquid or material it can hold.
- Unit Equivalence: One cubic centimeter (1 cm³) is exactly equivalent to one milliliter (1 mL). Therefore, a tank with a volume of 400 cm³ can hold 400 mL.
- Conversion to Liters: Since 1,000 mL equals 1 liter (L), 400 mL is equivalent to 0.4 liters.
This ability to convert between cubic units and liquid units makes volume calculations incredibly versatile for everyday and industrial applications.
