Surface Area of Cylinder | Curved and Total Surface Area of Cylinder (original) (raw)

Last Updated : 6 Aug, 2025

**Surface Area of a Cylinder is the amount of space covered by the flat surface of the cylinder's bases and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the cylinder's two circular bases as well as the area of the curving surface.

**The volume of a cylinder is calculated using the formula V = πr 2 h and its surface area is determined by SA = 2πrh + 2πr 2 . Let's apply these formulas to a sample problem to understand how to use them in practical calculations.

**This article will explore the surface area of the cylinder including the total surface area as well as the curved surface area, with their formulas, derivation of the formula, how to calculate surface area, and examples based on it.

Surface Area of Cylinder

Table of Content

**What is the Surface Area of Cylinder?

The surface area of a cylinder is the total area that covers its outer surface.

Let us imagine a cylindrical object, like a can or a pipe. To find its surface area, we need to consider two parts:

  1. **Curved Surface Area (CSA): This is the area of the curved side of the cylinder. You can think of it as if you were peeling off the label of a can. It's like the wrapper around the cylinder.
  2. **Two Circular Ends: A cylinder has two circular ends, one at the top and one at the bottom. Each of these circular ends has an area of πr2.

Surface Area of Cylinder Definition

The surface area of a cylinder refers to the total area that the surface of the cylinder occupies. This includes both the area of the curved surface (the lateral area) connecting the two circular bases and the areas of the two bases themselves.

**Surface Area of Cylinder Formula

Because a cylinder has a curved surface, we can express both its curved surface area and overall surface area.

Here are the formulas for the two types of surface areas of cylinder, with **radius = r and height = h.

Formula Value
Curved Surface Area of Cylinder 2πrh
Total Surface Area of Cylinder 2πr2 + 2πrh = 2πr(r + h)

Now, lets learn about both of them in detail.

**Curved Surface Area (CSA) of Cylinder

The curved surface area of the cylinder is enclosed between the two parallel circular bases. It is also known as the **lateral surface area.

**CSA of Cylinder Formula

The Curved Surface Area (CSA) of Cylinder formula is as follows:

**Curved Surface Area = 2πrh sq. units

where,

**Total Surface Area of Cylinder

A **total surface area of a cylinder is the sum of its curved surface area and the area of its two circular bases. It is calculated by **summing the areas of the two bases and the curved surface (CSA).

Total-Surface-Area-of-Cylinder

**Total Surface Area of Cylinder

The formula for Total Surface Area (TSA) of cylinder is given by,

**Total Surface Area of Cylinder = 2πr 2 + 2πrh = 2πr(r + h) sq. units

where,

**Derivation of Surface Area of Cylinder

Let us consider a cylinder whose radius is r and height is h. The cylinder is divided into three parts: one circular base at top, one rectangular curved area and another circular base at bottom.

Derivation of Surface Area of Cylinder Formula

Hence , the formula for the CSA of cylinder is given by

CSA of cylinder **= 2πrh

Now, the total surface area of the cylinder is the sum of above two areas.

A = A1 + A2

A = 2πr2 + 2πrh

**TSA of cylinder = 2πr(r + h)

This derives the formula for total surface area of a cylinder.

Difference between Total Surface Area and Curved Surface Area of Cylinder

The main differences between them Total Surface Area and Curved Surface Area are tabulated below.

Property Total Surface Area (TSA) of Cylinder Curved Surface Area (CSA) of Cylinder
Definition The total area of all the surface which includes the curved surface and the two base areas. It is defined as the area of the curved surface of the cylinder.
Formula The formula for TSA of the cylinder is, **TSA = 2πr (r + h) The formula for CSA of the cylinder is, **CSA = 2πrh
Relation TSA is greater than CSA as it includes CSA along with both the base areas. CSA is lesser than TSA.

How to Calculate Surface Area of Cylinder?

Surface area of a cylinder can be calculated using the steps added below,

**Step 1: Note the radius, 'r', and height, 'h' of cylinder. Remember both have the same units. Here, given r = 14 cm, h = 10 cm

**Step 2: Find the total surface area of the cylinder, the formula for the total surface area of the cylinder = 2πr(r + h)

**Step 3: Put the given values in the above formulas and find the answer in square units.

Surface Area of Cylinder in square meters

Let's find the total surface area of a cylinder that has a radius of 14 cm and a height of 10 cm.

Substitute the values in the formula we get,

Total Surface Area(TSA) = 2πr(r + h)

TSA = 2π × 14(14 + 10)

TSA = 2π × 336

TSA = 2 × 3.14 × 336

TSA = 2110.08 square cm

Surface Area of Cylinder in square feet

Let's calculate the **total surface area of a water tank with a radius of 4 feet and a height of 8 feet in square feet.

Substitute the values into the formula:

TSA = 2π × 4 × (4 + 8)

Now, let's calculate the values inside the brackets.

TSA = 2π × 4 × 12 = 96π square feet ≈ 96 × 3.14 square feet

≈ 301.44 square feet (rounded to two decimal places)

Volume of Cylinder

Volume of a cylinder is defined as the total amount of space occupied by the cylinder. For a cylinder of base radius r, and height h the volume is given by the formula,

**Volume of Cylinder = πr 2 h

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**Surface Area of Cylinder Examples

Let's solve some questions on the formulas of TSA and CSA of a cylinder.

**Example 1: Find the curved surface area of the cylinder of radius 3 cm and height of 7 cm.

**Solution:

Given,

Curved Surface Area of Cylinder(CSA) = 2πrh

CSA = 2 (22/7) (3) (7)

CSA = 2 (22) (3)

CSA = 132 cm2

**Example 2: Find the radius of the cylinder of curved surface area of 220 sq. cm and height of 7 cm.

**Solution:

Given,

Curved Surface Area of Cylinder(CSA) = 2πrh

220 = 2 (22/7) (r) (7)

220 = 44r

r = 220/44

r = 5 cm

**Example 3: Find the total surface area of the cylinder of radius 21 cm and height of 42 cm.

**Solution:

Given,

Total Surface Area(TSA) = 2πr2 + 2πrh

TSA = 2 (22/7) (21) (21) + 2 (22/7) (21) (42)

TSA = 2 (22) (3) (21) + 2 (22) (3) (42)

TSA = 2772 + 5544

TSA = 8316 sq. cm

**Example 4: Find the total surface of the cylinder if the curved surface area is 176 sq. cm and the height is 21 cm.

**Solution:

Given,

Curved Surface Area of Cylinder(CSA) = 2πrh

176 = 2 (22/7) (r) (21)

176 = 2 (22) (r) (3)

r = 176/132

r = 1.33 cm

Total Surface Area(TSA) = 2πr2 + 2πrh

TSA = 2 (3.14) (1.33) (1.33) + 176

TSA = 11.10 + 176

TSA = 187.1 sq. cm

Surface Area of Cylinder Class 8

For students in Class 8, understanding the surface area of a cylinder is an important part of geometry. This formula and calculation help students understand how much material would be needed to cover such a shape or how much paint might be required to coat it, making it applicable in real-world scenarios like construction and crafts.

**Important Maths Related Links:

Surface Area of Cylinder Practice Questions

Here is a worksheet on Surface Area of Cylinder for you to solve.

**Q1. If the Radius of a cylinder is 5 cm and the height of the cylinder is 15 cm. Find the curved area of the cylinder.

**Q2. If the Radius of a cylinder is 12 m and the height of the cylinder is 21 m. Find the total area of the cylinder.

**Q3. What is the radius of a cylinder with height of the cylinder is 21 cm and curved surface area 225 cm 2 ?

**Q4. What is the height of a cylinder with radius of the cylinder is 21 cm and curved surface area 105 cm 2 ?

Surface Area of Cylinder Summary

The surface area of a cylinder can be calculated using the formula **SA = 2πrh + 2πr 2, where r represents the radius of the cylinder's base and h is its height. This formula includes two parts: 2πrh accounts for the area of the cylindrical side (the lateral surface), and 2πr 2 adds the areas of the top and bottom circular faces. Understanding this calculation is crucial for practical applications, such as determining the amount of material needed to make a cylindrical object or calculating the surface area for painting or coating a cylinder.