Right Cylinder Calculator
Calculate volume, surface area, lateral area, and base area of a right circular cylinder
Calculate Cylinder Properties
Distance from center to edge of the circular base
Distance between the two circular bases
Cylinder Properties
Example Calculation
Water Tank Example
Radius: 5 cm
Height: 10 cm
Calculations
Volume: π × 5² × 10 = 785.4 cm³
Base Area: 2 × π × 5² = 157.1 cm²
Lateral Area: 2 × π × 5 × 10 = 314.2 cm²
Total Area: 157.1 + 314.2 = 471.2 cm²
Cylinder Components
Radius
Distance from center to edge
Used in all formulas
Height
Distance between bases
Perpendicular to base
Pi (π)
Mathematical constant ≈ 3.14159
Essential for circular calculations
Formula Reference
Understanding Right Cylinders
What is a Right Cylinder?
A right cylinder is a three-dimensional solid with two parallel circular bases connected by a curved lateral surface. The axis connecting the centers of the bases is perpendicular to both bases, making it "right."
Key Components
- •Two circular bases: Identical circles at top and bottom
- •Lateral surface: Curved surface connecting the bases
- •Radius (r): Distance from center to edge of base
- •Height (h): Distance between the two bases
Cylinder Formulas Explained
Volume Formula
V = π × r² × h
Volume equals the area of the circular base (πr²) multiplied by the height. This gives the amount of space inside the cylinder.
Surface Area Formula
A = 2πr(r + h)
Total surface area includes both circular bases (2πr²) plus the lateral surface area (2πrh).
Lateral Area Formula
A_l = 2πrh
The curved surface area when "unrolled" forms a rectangle with width = circumference (2πr) and height = h.
Real-World Applications
Engineering & Construction
- • Water tanks and storage containers
- • Pipes and tubing calculations
- • Concrete pillars and columns
- • Oil drums and barrels
Manufacturing
- • Material usage calculations
- • Packaging design optimization
- • Can and bottle production
- • Industrial equipment sizing
Science & Education
- • Laboratory equipment calculations
- • Physics and chemistry problems
- • Geometry education
- • Volume and capacity studies