A cylinder has a height of 10 cm and a base radius of 3 cm. Calculate its volume using \(\pi \approx 3.14\).
["# Understanding Cylinder Volume: A Complete Guide with an Example", "When studying geometry, one of the most fundamental shapes you encounter is the cylinder. Whether used in engineering, architecture, or everyday calculations, understanding how to compute a cylinder’s volume is essential. In this article, we’ll explore the basic formula for calculating the volume of a cylinder, followed by a practical example using a cylinder with a height of 10 cm and a base radius of 3 cm.", "## What Is a Cylinder?", "A cylinder is a three-dimensional geometric shape with two identical circular bases connected by a curved lateral surface. The height ((h)) of a cylinder is the perpendicular distance between the two bases. The base radius ((r)) is the distance from the center of the circular base to its edge.", "## Formula for Volume of a Cylinder", "The volume (V) of a cylinder is calculated using the formula:", "[\nV = \pi r^2 h\n]", "Where:\n- (r) = radius of the base (in cm)\n- (h) = height of the cylinder (in cm)\n- (\pi \approx 3.14) (a common approximation for easy calculation)", "## Applying the Formula: Example Calculation", "Let’s apply this formula using the given dimensions:\n- Height ((h)) = 10 cm\n- Base radius ((r)) = 3 cm\n- (\pi \approx 3.14)", "Step 1: Square the radius\n[\nr^2 = 3^2 = 9\n]", "Step 2: Multiply by height\n[\n9 \ imes 10 = 90\n]", "Step 3: Multiply by (\pi)\n[\nV \approx 3.14 \ imes 90 = 282.6\n]", "Thus, the volume of the cylinder is approximately 282.6 cubic centimeters.", "## Why Volume Matters", "Knowing how to calculate cylinder volume helps in various real-world applications—from determining how much liquid a container can hold to calculating structural material usage in cylindrical supports.", "## Summary", "For a cylinder with height 10 cm and base radius 3 cm:\n- Base area = (\pi r^2 = 3.14 \ imes 9 = 28.26 , \ ext{cm}^2)\n- Volume = Base area × height = (28.26 \ imes 10 = 282.6 , \ ext{cm}^3)", "Remember: Volume = (\pi r^2 h), and using (\pi \approx 3.14) simplifies quick estimation and classroom learning.", "Whether for academic work or practical projects, mastering cylinder volume calculations allows you to tackle a wide range of measurement challenges with confidence."]
