Curved Surface Area of Cylinder with Formula Examples

Curved Surface Area of Cylinder is the area of the outer curved part of a cylinder, excluding its circular bases. It is calculated using the radius and height. This page covers the formula, derivation, unit conversion, solved examples, common cases and shortcuts for quantitative aptitude problems.

On this page

What Is the Curved Surface Area of a Cylinder?

The curved surface area of a cylinder is the area of its lateral surface, without including the top and bottom circular faces. Its formula is CSA = 2πrh, where r is the radius and h is the height.

When the curved surface of a cylinder is opened out, it forms a rectangle. The rectangle's length is the circumference of the circular base, 2πr, and its breadth is the cylinder's height, h. Therefore, curved surface area = circumference × height = 2πr × h. The answer is expressed in square units.

Curved Surface Area of Cylinder Video Lessons

Watch short topic-wise lessons for quick revision.

8 Lessons
Lesson 1 of 8 Quick Revision

Cylinder Volume and Surface Area

Learn how to calculate a cylinder’s volume, curved surface area (CSA), and total surface area (TSA) using the relevant mensuration formulas.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More Curved Surface Area of Cylinder Lessons Scroll to explore →

Curved Surface Area of Cylinder Formula & Tricks

Important Formulas

Curved surface area
CSA = 2πrh

Here, r is the radius of the base and h is the perpendicular height of the cylinder.

Using diameter
CSA = πdh

If the diameter d is given, use r = d/2. Hence, 2πrh becomes πdh.

Using circumference
CSA = circumference of base × height = Ch

Since the base circumference C equals 2πr, the curved area can also be found as Ch.

Quick Tricks

Use the circumference-times-height method

The curved surface unwraps into a rectangle. Its length is the base circumference and its breadth is the height, so CSA = Ch.

Example: If the base circumference is 22 cm and the height is 10 cm, CSA = 22 × 10 = 220 cm².
Cancel factors before multiplying

When π = 22/7 and the radius or diameter contains a factor of 7, cancel first to reduce calculation time.

Example: For r = 7 cm and h = 10 cm, CSA = 2 × 22/7 × 7 × 10 = 440 cm².

Curved Surface Area of Cylinder Concepts

Derivation from the Unrolled Cylinder

The curved surface of a cylinder becomes a rectangle when unrolled, giving the formula CSA = 2πrh.

The rectangle has length equal to the circumference of the circular base, 2πr, and breadth equal to the cylinder's height, h. Multiplying these dimensions gives 2πr × h = 2πrh.

Example: For r = 5 cm and h = 12 cm, CSA = 2 × π × 5 × 12 = 120π cm², or approximately 377 cm².

Using Radius, Diameter and Height

The radius must be used in CSA = 2πrh; if diameter is provided, use CSA = πdh.

The radius is half the diameter, so d = 2r. For a cylinder with diameter 14 cm and height 20 cm, CSA = π × 14 × 20 = 280π cm². Using π = 22/7, the area is 880 cm².

Example: If d = 14 cm and h = 20 cm, CSA = (22/7) × 14 × 20 = 880 cm².

Units and Unit Conversion

Curved surface area is measured in square units, such as cm², m² or mm².

Convert radius and height into the same linear unit before applying the formula. If a length changes from metres to centimetres, multiply by 100; the corresponding area changes by a factor of 100².

Example: For r = 0.5 m and h = 2 m, CSA = 2π × 0.5 × 2 = 2π m², which is approximately 6.28 m².

Curved Surface Area and Total Surface Area

Curved surface area excludes both circular bases, while total surface area includes them.

The area of one circular base is πr². Therefore, total surface area is TSA = 2πrh + 2πr² = 2πr(h + r). Do not add the two bases when a question asks only for the curved surface area.

Example: For r = 3 cm and h = 8 cm, CSA = 48π cm², while TSA = 2π × 3 × (8 + 3) = 66π cm².

Curved Surface Area of Cylinder Visual Guide

Use the diagram or chart below to understand the concept clearly.

Cylinder with radius and height

Visual guide: Cylinder with radius and height
r: 5 cm h: 12 cm
The curved surface area depends on the base radius r and perpendicular height h.

Learn more concepts on PrepShots

Start ₹1 Trial →

Practice Curved Surface Area of Cylinder Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

Want more practice questions?

Practice in App →

Curved Surface Area of Cylinder Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

Curved Surface Area of Cylinder Revision Points

Use these formulas and rules for quick revision.

  • CSA = 2πrh.
  • If diameter d is given, CSA = πdh.
  • CSA also equals base circumference × height.
  • Curved surface area excludes the top and bottom circular bases.
  • Use square units for the answer.
  • Convert radius and height to the same unit before calculation.
  • TSA = 2πr(h + r), which includes both circular bases.

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Curved Surface Area of Cylinder FAQs

What is the curved surface area of a cylinder with radius 7 cm and height 10 cm?

CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².

What is the curved surface area formula when the diameter is given?

Use CSA = πdh, where d is the diameter and h is the height. This follows from r = d/2.

What is the curved surface area of a cylinder with diameter 14 cm and height 5 cm?

CSA = πdh = 22/7 × 14 × 5 = 220 cm².

Does curved surface area include the circular bases?

No. It includes only the lateral or outer curved surface. Both circular bases are included only in the total surface area.

What is the curved surface area if the circumference of the base is 30 cm and the height is 8 cm?

CSA = circumference × height = 30 × 8 = 240 cm².

What happens to the curved surface area if the radius is doubled while height remains constant?

The curved surface area doubles because CSA = 2πrh is directly proportional to r when h is constant.

Continue learning Curved Surface Area of Cylinder on PrepShots

Continue on PrepShots