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

0
cm³
Volume (V)
V = π × r² × h
0
cm²
Total Surface Area (A)
A = 2πr(r + h)
0
cm²
Lateral Surface Area (A_l)
A_l = 2πrh
0
cm²
Base Surface Area (A_b)
A_b = 2πr²
0
cm
Diameter (d = 2r)
0
cm
Circumference (C = 2πr)

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

r

Radius

Distance from center to edge

Used in all formulas

h

Height

Distance between bases

Perpendicular to base

π

Pi (π)

Mathematical constant ≈ 3.14159

Essential for circular calculations

Formula Reference

Volume
V = π × r² × h
Total Surface Area
A = 2πr(r + h)
Lateral Area
A_l = 2πrh
Base Area
A_b = 2πr²

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