Cylinder in Maths – Definition, Formulas, Examples & Applications

The concept of cylinder plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. From storing liquids in tanks to rolling cans, understanding cylinders helps students solve volume and surface area problems smoothly.

What Is Cylinder?

A cylinder is a 3-dimensional geometric solid with two parallel and congruent circular bases connected by a curved surface. You’ll find this concept applied in areas such as Mensuration, geometry, and real-life objects like pipes, cans, and tanks.

Key Formula for Cylinder

Here’s the standard formula:

Cross-Disciplinary Usage

Cylinder is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for JEE or NEET will see its relevance in various practical and theoretical questions.

Cylinder Properties

• 3D solid with two parallel, congruent circular bases
• Curved surface connects the two bases
• Height (h): Perpendicular distance between bases
• Radius (r): Distance from center to edge of the base
• Faces: 3 (2 circular, 1 curved)
• Edges: 2 (where the bases meet the curved part)
• No vertices (corners)
• Axis: line joining the centers of the bases
• Symmetry: Infinite lines of symmetry

How to Derive Cylinder Formulas

1. Curved Surface Area (CSA):
   
   Unroll the cylinder's side — it's a rectangle with height h and width equal to the circle's circumference (2πr).
   Area = Length × Height = 2πr × h = 2πrh
   
   
2. Total Surface Area (TSA):
   
   Add areas of top and bottom circles (πr² + πr² = 2πr²) to CSA.
   TSA = 2πrh + 2πr² = 2πr(r + h)
   
   
3. Volume:
   
   Volume = Area of base × Height = πr²h

Step-by-Step Illustration

1. Sample Problem: Find the volume and total surface area of a cylinder with radius 3 cm and height 7 cm.
2. Volume:
   V = πr²h = π × (3)² × 7 = π × 9 × 7 = π × 63 ≈ 3.14 × 63 = 197.82 cm³
   
   
3. Total Surface Area:
   TSA = 2πr(r + h) = 2 × π × 3 × (3 + 7) = 2 × π × 3 × 10 = 6π × 10 = 60π ≈ 188.4 cm²

Speed Trick or Vedic Shortcut

When a cylinder's diameter is given, halve to get the radius. For quick calculation: multiply radius × radius × height, then multiply by π (approx. 3.14). Estimation works well for MCQs.

Example Trick: For a cylinder with diameter 8 cm and height 5 cm:
1. r = 8 ÷ 2 = 4
2. 4 × 4 × 5 = 80
3. 80 × 3.14 ≈ 251.2 cm³ (volume)

Tricks like these help you save time in timed competitive exams. Vedantu sessions often offer similar tips so you can answer quickly and avoid falling for common mistakes.

Try These Yourself

• Find the curved surface area of a cylinder of radius 6 cm and height 10 cm.
• If the curved surface area is 132 cm² and height 7 cm, find the radius.
• Write any 3 objects around you shaped like cylinders.
• What is the difference between a prism and a cylinder?

Frequent Errors and Misunderstandings

• Forgetting to square the radius in volume formula
• Mixing up height and diameter
• Using the wrong formula for hollow cylinders
• Incomplete units (not writing cm² or cm³)
• Applying π as 3 instead of 3.14 (unless specified)

Relation to Other Concepts

The idea of cylinder connects closely with cube/cuboid and cone topics. Mastering cylinders helps you approach more advanced shapes and questions in mensuration and 3D geometry.

Classroom Tip

A quick way to remember cylinder formulas is “πr²h for Volume, 2πrh for Curved Surface Area, and 2πr(r+h) for Total Area.” Imagine rolling a paper to form a cylinder—you see the circle (base) and rectangle (side) come together! Vedantu’s teachers often use simple objects in class—like cans or glass jars—to reinforce the concept visually during live classes.

We explored cylinder—from definition, formula, examples, mistakes, and connections to other math shapes. Continue practicing with Vedantu to become confident in solving problems involving cylinders quickly and correctly.

Related Topics on Vedantu

• Volume of Cube, Cuboid and Cylinder – Understand how cylinder formulas compare to other 3D shapes.
• Surface Area of Cylinder – A deep dive into curved and total surface areas with more solved problems.
• Right Circular Cylinder – Learn about the most tested cylinder type in exams.
• Cone, Sphere, Cylinder – See side-by-side comparisons and solve mixed shape questions.