Original volume \(V = \pi r^2 h = \pi (3)^2 (10) = 90\pi\) cubic cm.

["Original Volume Calculation: How to Compute the Volume of a Cylinder Using (V = \pi r^2 h)", "Understanding the volume of a cylinder is essential in mathematics, engineering, architecture, and everyday applications involving three-dimensional shapes. One of the foundational formulas used for calculating the volume of a cylinder is:", "[\nV = \pi r^2 h\n]", "where:\n- ( V ) = Volume in cubic centimeters (cm³)\n- ( r ) = Radius of the circular base in centimeters\n- ( h ) = Height or height of the cylinder in centimeters\n- ( \pi ) ≈ 3.1416 (a constant used in circular calculations)", "### Applying the Formula to a Specific Example", "Consider a cylinder with a radius of ( r = 3 ) cm and a height of ( h = 10 ) cm. Applying the volume formula step-by-step:", "[\nV = \pi r^2 h = \pi (3)^2 (10)\n]", "First, compute the square of the radius:\n[\n3^2 = 9\n]", "Next, multiply by the height:\n[\n9 \ imes 10 = 90\n]", "Then multiply by ( \pi ):\n[\nV = 90\pi \ ext{ cm}^3\n]", "### Why This Formula Works", "The volume of a cylinder represents the amount of space enclosed within its circular base and extended vertically. By squaring the radius and multiplying by height, the formula accounts for both the base area (( \pi r^2 )) and the thickness (height) of the solid.", "### Real-World Applications", "Knowing how to calculate cylindrical volume is practical in many contexts:", "- Engineering: Designing cylindrical tanks, pipes, and structural columns\n- Manufacturing: Manufacturing containers, weared rings, and mechanical parts\n- Architecture: Calculating materials for cylindrical pillars or water tanks\n- Everyday Life: Estimating the capacity of vegetable cans, compost bins, and water bottles", "### Final Result", "Thus, the original volume of a cylinder with radius 3 cm and height 10 cm is precisely:", "[\n\boxed{90\pi \ ext{ cm}^3}\n]", "This value approximately equals ( 90 \ imes 3.1416 \approx 282.74 ) cm³, making it straightforward to convert or use in practical scenarios.", "---", "Summary:\nUsing the formula ( V = \pi r^2 h ), the original volume of a cylinder with radius 3 cm and height 10 cm is ( 90\pi ) cubic centimeters — a fundamental calculation essential for STEM fields and daily measurement tasks."]