Surface Area of a Cylinder

The surface area of a cylinder is the total area occupied by all its outer surfaces, including the curved surface and the two circular bases. It represents the complete exterior covering of the cylinder and is measured in square units.

The surface area of a cylinder is divided into two components:

Curved Surface Area of a Cylinder (CSA)

The curved surface area (CSA) is the area covered by its curved outer surface, excluding the top and bottom circular bases. It represents the lateral covering of the cylinder.

For a cylinder with radius r and height h:

Curved Surface Area (CSA) = 2πrh square units

where

• r = radius,
• h = height,
• π ≈ 3.14 or 22/7

Total Surface Area of a Cylinder (TSA)

The total surface area is the sum of the areas of its two circular bases and its curved surface. It represents the complete outer covering of the cylinder.

The above figure shows how a cylinder can be opened into a rectangle along with two circular bases.

• The rectangle represents the curved surface, where its length is equal to the circumference of the base (2πr) and its height is h. Hence, the curved surface area is 2πrh.
• The two circles represent the bases, each having an area of πr². Adding these areas gives the total surface area of the cylinder as 2πr² + 2πrh.

For a cylinder with radius r and height h:

Total Surface Area (T.S.A) = 2πrh + 2πr² = 2πr(h+r) square units.

Where,

• h is Height
• r is Radius of Cylinder

Example: Find the total surface area of a cylinder with radius 5 cm and height 8 cm.

Solution:

TSA = 2πr(r + h)
= 2 × 3.14 × 5 × (5 + 8)
= 408.4 cm² (approx.)

Related Articles

• Cylinder Shape
• Surface Area of Cylinder 
• Volume of a Cylinder

Sample Problems

Problem 1: Compute the total surface area of the cylinder with a radius of 5 cm and a height of 10 cm.

Solution:

Since, we know, 

Total surface area of a cylinder, A = 2πr(r+h) square units

Therefore, A = 2π × 5(5 + 10) = 2π × 5(15) 

= 2π × 75 = 150 × 3.14 

= 471 cm²

Problem 2: A cylinder has a radius of 7 cm and a height of 20 cm. A thin sheet is used to cover the entire outer surface of the cylinder. Find the total surface area required.

Solution:

Given: r = 7 cm, h = 20 cm

TSA = 2πr(r + h)
= 2 × (22/7) × 7 × (7 + 20)
= 2 × 22 × 27
= 1188 cm²

Problem 3: A cylindrical pipe has an inner radius of 5 cm and a height of 28 cm. Only the outer curved surface is to be painted. Find the curved surface area to be painted.

Solution:

Given: r = 5 cm, h = 28 cm

CSA = 2πrh
= 2 × (22/7) × 5 × 28
= 2 × 22 × 5 × 4
= 880 cm²

Problem 4: A water tank has a radius of 40 inches and a height of 150 inches. Find the area. 

Solution:

Water tank is cylindrical in nature. 

Total Surface Area of a cylinder is given by,  2πr(h+r)

TSA = 2 × 22/7 × 40(150 + 40)

TSA = 2 × 22/7 × 40 × 190

TSA = 440/7 × 7600

TSA = 3344000/ 7

Area = 47,7142.857 sq.inches.

Problem 5: The height of a cylinder is twice its radius. If the radius is 6 cm, find the total surface area of the cylinder.

Solution:

Given: r = 6 cm, h = 2r = 12 cm

TSA = 2πr(r + h)
= 2 × 3.14 × 6 × (6 + 12)
= 2 × 3.14 × 6 × 18
= 2 × 3.14 × 108
= 678.24 cm²