To find the total surface area of a cylinder i.e., TSA we use the formula TSA of cylinder = 2πr (h + r). In this article we will explore how to find the total surface area of a cylinder along with the different ways to find total surface area of cylinder. We will also solve some examples related to total surface area of cylinder. Let’s start our learning on the topic “How to Find the Total Surface Area of a Cylinder.”

What is Total Surface Area of a Cylinder?

The total surface area of a cylinder is the surface area covered by curved surface and circular bases of the cylinder. In other words, the total surface area of a cylinder is given by the sum of the area of curved surface and the area of the two circular bases.

How to Find the Total Surface Area of a Cylinder

To find the total surface area of a cylinder we use the total surface area of the cylinder formula according to the dimensions given in the questions. The below are some steps to find the total surface area of a cylinder.

• First, identify the dimensions of cylinder given in the question.
• Then, according to the dimensions apply the formula for TSA.
• The resultant value gives the total surface area of a cylinder

Total Surface Area of a Cylinder Formula

The different formulas for the total surface area of a cylinder are listed below.

Total Surface Area with Radius and Height of Cylinder

The total surface area with radius and height of cylinder is given by:

Total Surface Area of Cylinder = 2πrh + 2πr²

where,

• r is radius of cylinder
• h is height of cylinder

Total Surface Area with Diameter and Height of Cylinder

The total surface area with diameter and height of cylinder is given by:

Total Surface Area of Cylinder = πdh + (πd²) / 2

where,

• d is diameter of cylinder
• h is height of cylinder

Total Surface Area with Curved Surface Area and Radius of Cylinder

The total surface area with curved surface area and radius of cylinder is given by:

Total Surface Area of Cylinder = CSA + 2πr²

Where,

• CSA is curved surface area of cylinder
• r is radius of cylinder

Total Surface Area with Curved Surface Area and Area of Base

The total surface area with curved surface area and area of base is given by:

Total Surface Area of Cylinder = CSA + 2 × A

where,

• CSA is curved surface area of cylinder
• A is area of base (since, the cylinder has 2 bases we have multiplied A with 2)

Related Articles

• Surface Area of Cylinder
• Volume of a Cylinder
• Area of Hollow Cylinder

Examples on How to Find Total Surface Area of a Cylinder

Example 1: Calculate the total surface area of cylinder if the radius of cylinder is 8 units and the height of cylinder is 20 units.

Solution:

To find the total surface area of given cylinder we use formula:

Total Surface Area of Cylinder = 2πrh + 2πr²

Total Surface Area of Cylinder = (2π) × (8) × (20) + 2π × 8²

Total Surface Area of Cylinder = 80π + 128π

Total Surface Area of Cylinder = 208π sq. units

Example 2: Find the total surface area of cylinder if the diameter of base is 10 units and the height of the cylinder is 15 units.

Solution:

To find the total surface area of given cylinder we use formula:

Total Surface Area of Cylinder = πdh + (πd²) / 2

Total Surface Area of Cylinder = π× 10 × 15 + (π×10²) / 2

Total Surface Area of Cylinder = 150π + (100π) / 2

Total Surface Area of Cylinder = 150π + 50π

Total Surface Area of Cylinder = 200π sq. units

Example 3: Determine the total surface area of cylinder if the curved surface area of cylinder is 18 sq. units and the radius is 4 units.

Solution:

To find the total surface area of given cylinder we use formula:

Total Surface Area of Cylinder = CSA + 2πr²

Total Surface Area of Cylinder = 18 + 2π(4)²

Total Surface Area of Cylinder = 18 + 32π

Total Surface Area of Cylinder = 118.53 sq. units

Example 4: Find the total surface area of cylinder given the curved surface area is 12 sq. units and area of base is 10 sq. units.

Solution:

To find the total surface area of given cylinder we use formula:

Total Surface Area of Cylinder = CSA + 2 × A

Total Surface Area of Cylinder = 12 + 2 × 10

Total Surface Area of Cylinder = 12 + 20

Total Surface Area of Cylinder = 32 sq. units

Practice Problems on Total Surface Area of a Cylinder

Q1. Calculate the total surface area of cylinder if the radius of cylinder is 80 units and the height of cylinder is 110 units.

Q2. Find the total surface area of cylinder if the diameter of base is 52 units and the height of the cylinder is 75 units.

Q3. Determine the total surface area of cylinder if the curved surface area of cylinder is 250 sq. units and the radius is 32 units.

Q4. Find the total surface area of cylinder given the curved surface area is 130 sq. units and area of base is 50 sq. units.

FAQs on How to Find Total Surface Area of a Cylinder

What is the formula to find the total surface area of a cylinder?

The formula to find the total surface area of a cylinder is given by:

TSA of Cylinder = 2πrh + 2πr²

What is the curved surface area of a cylinder formula?

The curved surface area of a cylinder formula is given by: CSA = 2πrh

What is the formula for total surface area of hollow cylinder?

The formula for total surface area of hollow cylinder is given by: TSA = 2πh(R + r) + 2π(R² – r²)

Is curves surface area and total surface area of cylinder are same?

No, the curved surface area and total surface area of cylinder are not same. CSA includes area of curved surface while TSA include CSA and area of top and bottom.