Surface area of cylinders

Calculate the curved surface area and total surface area of cylinders, including open cylinders and real-world applications.

Worked examples

Curved surface area of a cylinder

Straightforward

Problem

Find the curved surface area of a cylinder with radius

6 \text{ cm}

and height

8 \text{ cm}

. Round your answer to 2 decimal places.

Total surface area of a closed cylinder

Moderate

Problem

Find the total surface area of a closed cylinder with radius

5 \text{ cm}

and height

10 \text{ cm}

. Round your answer to 2 decimal places.

Surface area of an open cylindrical tin

Challenging

Problem

A cylindrical tin has no lid. Its radius is

6 \text{ cm}

and its height is

10 \text{ cm}

. Find the total surface area of material needed to make the tin. Round your answer to 2 decimal places.

Practise

Q1·Straightforward

Find the curved surface area of a cylinder with radius

3 \text{ cm}

and height

10 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q2·Straightforward

Find the curved surface area of a cylinder with radius

5 \text{ cm}

and height

8 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q3·Straightforward

Find the curved surface area of a cylinder with radius

2 \text{ cm}

and height

7 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q4·Straightforward

Find the curved surface area of a cylinder with radius

4 \text{ cm}

and height

6 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q5·Moderate

Find the total surface area of a closed cylinder with radius

4 \text{ cm}

and height

9 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q6·Moderate

Find the total surface area of a closed cylinder with radius

3 \text{ cm}

and height

6 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q7·Moderate

Find the total surface area of a closed cylinder with radius

7 \text{ cm}

and height

12 \text{ cm}

. Give your answer in

\text{cm}^2

rounded to 2 decimal places.

Q8·Moderate

A closed cylindrical drum has a diameter of

10 \text{ cm}

and a height of

15 \text{ cm}

. Find its total surface area in

\text{cm}^2

rounded to 2 decimal places.

Q9·Challenging

A cylindrical storage tin has no lid. The radius is

5 \text{ cm}

and the height is

12 \text{ cm}

. Find the total surface area of material needed to make the tin in

\text{cm}^2

rounded to 2 decimal places.

Q10·Challenging

A label is to be wrapped tightly around the outside of a cylindrical can. The can has a diameter of

8 \text{ cm}

and a height of

14 \text{ cm}

. Find the area of the label in

\text{cm}^2

rounded to 2 decimal places.

Q11·Challenging

A length of metal pipe is open at both ends. It has a radius of

3 \text{ cm}

and a length of

20 \text{ cm}

. Find the area of metal used to make the pipe in

\text{cm}^2

rounded to 2 decimal places.

Q12·Challenging

A concrete pillar is a solid cylinder with a diameter of

1.2 \text{ m}

and a height of

3 \text{ m}

. Calculate the total surface area of the pillar (including both circular ends) in

\text{m}^2

rounded to 2 decimal places.