The exact volume of the cylinder is 2310 cm³.
Calculating the volume of a cylinder is a straightforward process when you have the necessary dimensions. In this specific case, we are provided with the cross-sectional area and the height, which are the two critical components for this calculation.
Understanding Cylinder Volume
The volume of any prism, including a cylinder, is determined by multiplying its base (cross-sectional) area by its height. This fundamental principle simplifies many geometric calculations.
The formula for the volume of a cylinder is:
$$V = A \times h$$
Where:
- $V$ is the volume of the cylinder.
- $A$ is the cross-sectional area (or base area) of the cylinder.
- $h$ is the height of the cylinder.
For a deeper dive into cylinder geometry, you can explore resources like Khan Academy on Cylinder Volume.
Step-by-Step Calculation
Let's apply the formula using the given information:
- Cross-sectional Area (A): 154 cm²
- Height (h): 15 cm
-
Identify the Given Values:
- Area ($A$) = 154 cm²
- Height ($h$) = 15 cm
-
Apply the Volume Formula:
- $V = A \times h$
- $V = 154 \text{ cm}^2 \times 15 \text{ cm}$
-
Perform the Multiplication:
- $V = 2310 \text{ cm}^3$
The calculation clearly shows that multiplying the cross-sectional area by the height yields the total volume occupied by the cylinder.
Summary of Dimensions and Volume
To make the information easily digestible, here's a quick reference table:
| Dimension | Value | Unit |
|---|---|---|
| Cross-sectional Area | 154 | cm² |
| Height | 15 | cm |
| Calculated Volume | 2310 | cm³ |
Practical Applications of Cylinder Volume
Understanding how to calculate cylinder volume is not just an academic exercise; it has numerous real-world applications:
- Engineering: Designing pipes, storage tanks, and engine cylinders.
- Construction: Estimating the amount of concrete needed for cylindrical pillars or the capacity of water tanks.
- Manufacturing: Determining the material required for cylindrical components or the capacity of containers.
- Everyday Life: Knowing the volume of a can of soda, a water bottle, or even a swimming pool can be useful.
For instance, if you were an engineer designing a water storage tank, knowing its cross-sectional area and desired height would immediately tell you its maximum storage capacity.
Key Takeaway
The volume of a cylinder is a direct product of its base area and its height. This fundamental principle is widely applicable in various fields, making it an essential concept in geometry and practical problem-solving.
