Total Surface Area of Cylinder: Formula, Examples and Questions

Total Surface Area of Cylinder is the sum of the curved surface area and the areas of its two circular bases. The standard formula is 2πr(h + r), where r is the radius and h is the height. This page covers the formula, solved examples, units, shortcuts and common cylinder problems.

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What Is the Total Surface Area of a Cylinder?

The total surface area of a closed cylinder is the sum of its curved surface area and the areas of its two circular bases. Its formula is TSA = 2πr(h + r).

For a cylinder with radius r and height h, the curved surface area is 2πrh, while the two circular bases together have area 2πr². Therefore, TSA = 2πrh + 2πr² = 2πr(h + r). The answer is expressed in square units. For example, if r = 3 cm and h = 5 cm, TSA = 2 × π × 3 × 8 = 48π cm².

Total Surface Area of Cylinder Video Lessons

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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.

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Total Surface Area of Cylinder Formula & Tricks

Important Formulas

Total surface area using radius
TSA = 2πr(h + r)

Use r for the radius and h for the height of a closed cylinder.

Total surface area using diameter
TSA = πd(h + d/2)

Since r = d/2, this form can be used when the diameter d is given.

Component formula
TSA = CSA + 2πr² = 2πrh + 2πr²

The total area consists of the curved surface and two equal circular bases.

Quick Tricks

Add the curved surface and two bases

Remember TSA = CSA + two circular bases. Thus, TSA = 2πrh + 2πr² = 2πr(h + r).

Example: For r = 7 cm and h = 10 cm, TSA = 2 × 22/7 × 7 × 17 = 748 cm².
Convert diameter before substitution

If the diameter is given, divide it by 2 to obtain the radius before using 2πr(h + r).

Example: For diameter 14 cm and height 10 cm, r = 7 cm, so TSA = 748 cm² using π = 22/7.
Use consistent units

Convert radius and height to the same unit before calculating. The final unit is squared.

Example: If r = 50 cm and h = 2 m, convert h to 200 cm before finding the area.

Total Surface Area of Cylinder Concepts

Curved Surface Area and Circular Bases

A closed cylinder has one curved surface and two circular bases, so its total surface area is CSA + 2πr².

The curved surface area is CSA = 2πrh. Each base is a circle of area πr², so both bases have area 2πr². Adding them gives TSA = 2πrh + 2πr².

Example: For r = 4 cm and h = 6 cm, CSA = 2π × 4 × 6 = 48π cm², and the two bases have area 2π × 4² = 32π cm². Hence TSA = 80π cm².

Using Radius and Height

When radius and height are known, substitute them directly into TSA = 2πr(h + r).

First calculate h + r, then multiply by 2πr. Use π = 22/7 when the radius is a multiple of 7, or use π = 3.14 when specified.

Example: For r = 7 cm and h = 10 cm, TSA = 2 × 22/7 × 7 × (10 + 7) = 748 cm².

Using Diameter

When diameter d is given, the radius is d/2, and TSA can be written as πd(h + d/2).

The diameter is twice the radius. Substituting r = d/2 into 2πr(h + r) gives TSA = πd(h + d/2).

Example: For d = 10 cm and h = 12 cm, TSA = π × 10 × (12 + 5) = 170π cm².

Closed and Open Cylinders

The standard total surface area formula includes both circular bases and applies to a closed cylinder.

For a cylinder open at one end, the area is CSA + one base = 2πrh + πr². For a cylinder open at both ends, only the curved surface is counted: 2πrh.

Example: For r = 3 cm and h = 5 cm, a closed cylinder has TSA = 48π cm², while a cylinder open at one end has area 2π × 3 × 5 + 9π = 39π cm².

Total Surface Area of Cylinder Visual Guide & Data

Use the table and chart below to understand the data better.

Cylinder Surface Area Formulas

Comparison of the main surface-area expressions for a cylinder.

Surface type Formula Included parts
Curved surface area 2πrh Curved surface only
One circular base πr² One circular end
Two circular bases 2πr² Both circular ends
Total surface area 2πr(h + r) Curved surface and both ends

Note: All dimensions must use the same unit, and the result is expressed in square units.

Closed Cylinder with Radius and Height

Visual guide: Closed Cylinder with Radius and Height
Radius: r Height: h
A closed cylinder has two circular bases of radius r and a perpendicular height h.

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Practice Total Surface Area of Cylinder Questions

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1An article is sold for a profit of 50 percent. What is the ratio of the selling price of the article to the cost price of the article?→ 2A and B invest ₹4,000 and ₹6,000, respectively, for one year. The total profit is ₹5,000. What is the share of B?→ 3In an election with three candidates, M, N and R, candidate M secured 42% of the total votes, while candidate R obtained 34%. If the total number of votes polled was 37,700 and all were valid, how many votes did candidate N receive?→ 4Two-thirds of a consignment was sold at a profit of 6% and the rest at a loss of 3%. If there was an overall profit of Rs 540, find the value of the consignment.→ 5Find the HCF (Highest Common Factor) of:6/50, 24/20, 15/25→ 6Find the value of k in the given expression. (81)^(5-2k) × 3³ - 51⁰ = 2187 - 5⁰→ 7A man spends 30% of his salary on rent, 20% on groceries, and 25% on other expenses. If he saves Rs. 9,000, what is his salary?→ 8Calculate the sum of all the digits which are even numbers (repeating digits must be considered only once) in the number 788934754.→ 973P2 is divisible by 8. Which of the following cannot be the value of P?→ 10In an election, there are three candidates: A, B, and C. Candidate A gets 40% of the total valid votes, Candidate B gets 30%, and Candidate C gets the remaining votes. If 12% of the total votes were declared invalid and the total number of voters was 25,000, find the number of votes received by Candidate C.→

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Quick Revision Notes

Total Surface Area of Cylinder: Revision Points

Use these formulas and rules to revise the calculation of a cylinder's complete outer surface.

  • TSA of a closed cylinder = 2πr(h + r).
  • Curved surface area = 2πrh.
  • Area of two circular bases = 2πr².
  • If diameter d is given, radius r = d/2 and TSA = πd(h + d/2).
  • For a cylinder open at one end, area = 2πrh + πr².
  • Use the same unit for radius and height; the answer is in square units.

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 →

Total Surface Area of Cylinder FAQs

What is the total surface area of a cylinder formula?

For a closed cylinder, TSA = 2πr(h + r), where r is the radius and h is the height.

How do you find the total surface area when the diameter is given?

First use r = d/2. Alternatively, use TSA = πd(h + d/2).

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

Using π = 22/7, TSA = 2 × 22/7 × 7 × 17 = 748 cm².

Does total surface area include both circular bases?

Yes. For a closed cylinder, total surface area includes the curved surface and both circular bases: 2πrh + 2πr².

What is the difference between curved surface area and total surface area of a cylinder?

Curved surface area is 2πrh and excludes the bases. Total surface area is 2πrh + 2πr² and includes both bases.

What is the surface area of a cylinder open at one end?

It is 2πrh + πr² because it includes the curved surface and only one circular base.

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