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Math resources Geometry Surface area

Surface area of a cylinder

Surface area of a cylinder

Here you will learn about the surface area of a cylinder, including how to calculate the lateral surface area of a cylinder given its radius and its perpendicular height.

Students will first learn about the surface area of a cylinder as part of geometry in th grade.

What is the surface area of a cylinder?

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

In order to calculate the total surface area of a cylinder you need to find the area of the three parts of the surface and add them together.

There is a lateral surface area and two circular bases.

(The lateral surface area of a cylinder is also referred to as the curved surface area of a cylinder).

Surface area of a cylinder 1 US

Surface area of a cylinder 2 US

r r is the radius of the cylinder. The lateral surface area of a cylinder is a rectangle.

The circumference of the circle is the length of the rectangle. The height of a cylinder h h is the height of the rectangle.

TOTAL surface area=2πrh+πr2+πr2=2πrh+2πr2 \begin{aligned}\text{TOTAL surface area}&=2\pi rh + \pi r^2 + \pi r^2 \\\\ &=2\pi rh+2\pi r^2\end{aligned}

Note: The examples on this page are for right circular cylinders. However, the formula above can be used for oblique cylinder if slant height is used for the value of h. h.

Let’s look at each part of the surface of a cylinder.

Lateral surface area

The lateral surface area of a cylinder is a rectangle.

Surface area of a cylinder 3 US

 base × height  \text { base } \times \text { height } is the formula for the area of the rectangle.

The base of the rectangle is the circumference of the circle:

Circumference of a circle=πd=2πr \text{Circumference of a circle}=\pi d=2\pi r

The height of the rectangle is height of the cylinder given by h. h.

To find the area of a rectangle you need to multiply the base 2πr 2\pi r by the height h. h.

This gives us the formula for the lateral surface area of a cylinder:

Lateral surface area=2πrh \text{Lateral surface area}=2\pi rh

Base area

Then you need to calculate the area of the base of the cylinder, this is a circle.

Formula for the area of circle:

Area of a circle=πr2 \text{Area of a circle}=\pi r^2

The area of the top and the area of the base of a cylinder are the same.

Total surface area of a cylinder

So to find the total surface area, you can add the lateral surface area to the area of the two circles:

TOTAL surface area=2πrh+πr2+πr2=2πrh+2πr2 \begin{aligned}\text{TOTAL surface area}&=2\pi rh+\pi r^2+ \pi r^2 \\\\ &=2\pi rh+2\pi r^2\end{aligned}

For example,

Calculate the total surface area of this cylinder with radius of the base 7cm 7 \, cm and perpendicular height 10cm. 10 \, cm.

Surface area of a cylinder 4 US

First, you need to find the lateral surface area of the cylinder:

Lateral surface area=2πrh=2×π×7×10=140π. \text{Lateral surface area}=2\pi rh=2\times \pi \times 7 \times 10=140\pi.

You then need to find the area of the base of the cylinder:

Area of a circle=πr2=π×72=49π. \text{Area of a circle}=\pi r^2=\pi \times 7^2=49\pi.

The area of the top of the cylinder is the same as the area of the base so,

Total surface area: 140π+49π+49π=238π=747.699905 140 \pi+49 \pi+49 \pi=238 \pi=747.699905 \ldots

Since the measurements of the cylinder are in cm, the surface area will be measured in cm2. cm^2.

The surface area of the cylinder is 747.7 cm2, 747.7 \mathrm{~cm}^2, rounded to the nearest tenth.

What is the surface area of a cylinder?

What is the surface area of a cylinder?

Common Core State Standards

How does this relate to 8 8 th grade math?

  • Grade 8 – Geometry (8.G.C.9)
    Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

[FREE] Surface Area Check for Understanding Quiz (Grade 6)

[FREE] Surface Area Check for Understanding Quiz (Grade 6)

[FREE] Surface Area Check for Understanding Quiz (Grade 6)

Use this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!

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[FREE] Surface Area Check for Understanding Quiz (Grade 6)

[FREE] Surface Area Check for Understanding Quiz (Grade 6)

[FREE] Surface Area Check for Understanding Quiz (Grade 6)

Use this quiz to check your grade 6 students’ understanding of surface area. 10+ questions with answers covering a range of 6th grade surface area topics to identify areas of strength and support!

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How to calculate the surface area of a cylinder

In order to calculate the surface area of a cylinder:

  1. Calculate the area of each face.
  2. Add the areas together.
  3. Write the answer, including the units.

Surface area of a cylinder examples

Example 1: lateral surface area (lsa)

Calculate the lateral surface area of the cylinder below, with radius 3cm 3 \, cm and perpendicular height 8cm. 8 \, cm.

Round your answer to the nearest tenth.

Surface area of a cylinder 5 US

  1. Calculate the area of each face.

This question is only asking us for the lateral surface area, so you only need to find the area of the curved surface that is between the circular bases.

Lateral surface area =2πrh=2×π×3×8=150.7964474 \begin{aligned}\text{Lateral surface area }&=2\pi rh\\\\ &=2 \times \pi \times 3 \times 8 \\\\ &=150.7964474…\end{aligned}

2Add the areas together.

Since you are only calculating the lateral surface area, you do not need to add any other areas.

3Write the answer, including the units.

You need to round the answer to the nearest tenth and include the units – square centimeters.

The lateral surface area of the cylinder is: 150.8 cm2. 150.8 \mathrm{~cm}^2.

Example 2: lateral surface area – in terms of π

Calculate the lateral surface area of the cylinder below, with radius 5inches 5 \, inches and perpendicular height 8inches. 8 \, inches.

Leave your answer in terms of π. \pi.

Surface area of a cylinder 6 US

Calculate the area of each face.

Add the areas together.

Write the answer, including the units.

Example 3: total surface area (tsa)

Calculate the surface area of the cylinder below, with radius 4cm 4 \, cm and perpendicular height 9cm. 9 \, cm.

Round your answer to the nearest whole.

Surface area of a cylinder 7 US

Calculate the area of each face.

Add the areas together.

Write the answer, including the units.

Example 4: decimal radius of a cylinder

Calculate the surface area of the cylinder below.

Round your answer to the nearest whole number.

Surface area of a cylinder 10 US

Calculate the area of each face.

Add the areas together.

Write the answer, including the units.

Example 5: total surface area (tsa)

Calculate the surface area of the cylinder below.

Leave your answer in terms of π. \pi.

Surface area of a cylinder 11 US

Calculate the area of each face.

Add the areas together.

Write the answer, including the units.

Example 6: total surface area (tsa)

Calculate the surface area of the cylinder below.

Leave your answer in terms of π. \pi.

Surface area of a cylinder 12 US

Calculate the area of each face.

Add the areas together.

Write the answer, including the units.

Teaching tips for surface area of a cylinder

  • Before using worksheets, give students opportunities to work with real world cylindrical shapes, like aluminum cans or food canisters. Have them estimate what they think the surface area is and then brainstorm ways to measure. Finally, introduce the formula and have students compare it to their estimate and brainstorming ideas.

  • Have students compare how calculating the surface area of a cylinder is similar and different from calculating the surface area of other 3 3 -dimensional shapes.

  • Calculating the surface area of a cylinder can extend beyond math classes and be applied to activities in science classes, art classes, and beyond. When teaching this topic, be sure that other teachers who work with your students are aware that this is something they can integrate into their curriculum as well.

Easy mistakes to make

  • Rounding too soon
    It is important to not round the answer until the end of the calculation. Rounding beforehand can make your answer less precise.

  • Confusing the radius or the diameter
    It is a common error to mix up radius and diameter. Remember, the radius is half of the diameter, and the diameter is double the radius.

    Surface area of a cylinder 13 US

  • Not using the correct units
    For area, you use square units such as cm2. \mathrm{cm}^2. For volume, you use cube units such as cm3. \mathrm{cm}^3.

Practice surface area of a cylinder questions

1. Calculate the lateral surface area of a cylinder with the radius of 5.2cm 5.2 \, cm and the perpendicular height of 8.3cm. 8.3 \, cm.

 

Round your answer to the nearest whole number.

 

Surface area of a cylinder 14 US

272cm2 272 \, cm^2
GCSE Quiz False

273cm2 273 \, cm^2
GCSE Quiz False

271cm2 271 \, cm^2
GCSE Quiz True

274cm2 274 \, cm^2
GCSE Quiz False

You are calculating the lateral surface area of a cylinder, so you substitute the values of r r and h h into the formula.

 Lateral surface area =2πrh=2×π×5.2×8.3=271.182=271 cm2 \begin{aligned}\text { Lateral surface area } & =2 \pi r h \\\\ & =2 \times \pi \times 5.2 \times 8.3 \\\\ & =271.182 \ldots \\\\ & =271 \mathrm{~cm}^2\end{aligned}

2. Calculate the lateral surface area of a cylinder with the radius of 6.7cm 6.7 \, cm and the perpendicular height of 4.9cm. 4.9 \, cm.

 

Round your answer to the nearest whole number.

 

Surface area of a cylinder 15 US

690cm2 690 \, cm^2
GCSE Quiz False

659cm2 659 \, cm^2
GCSE Quiz False

692cm2 692 \, cm^2
GCSE Quiz False

691cm2 691 \, cm^2
GCSE Quiz True

You are calculating the lateral surface area of a cylinder, so you substitute the values of r r and h h into the formula.

 

 Lateral surface area =2πrh=2×π×6.7×4.9=691.027=691 cm2 \begin{aligned}\text { Lateral surface area } & =2 \pi r h \\\\ & =2 \times \pi \times 6.7 \times 4.9 \\\\ & =691.027 \ldots \\\\ & =691 \mathrm{~cm}^2\end{aligned}

3. Calculate the lateral surface area of the cylinder below.

 

Leave your answer in terms of π. \pi.

 

Surface area of a cylinder 16 US

22πcm2 22\pi \, cm^2
GCSE Quiz False

28πcm2 28\pi \, cm^2
GCSE Quiz True

24πcm2 24\pi \, cm^2
GCSE Quiz False

26πcm2 26\pi \, cm^2
GCSE Quiz False

You are calculating the lateral surface area of a cylinder, so you substitute the values of r r and h h into the formula.

 

Lateral surface area=2πrh=2×π×2×7=28π=28π cm2 \begin{aligned}\text{Lateral surface area}&=2\pi rh \\\\ &=2 \times \pi \times 2\times 7 \\\\ &=28\pi \\\\ &=28\pi \ cm^2\\\end{aligned}

4. Calculate the surface area of the cylinder below.

 

Round your answer to the nearest whole number.

 

Surface area of a cylinder 17 US

384cm2 384 \, cm^2
GCSE Quiz False

254cm2 254 \, cm^2
GCSE Quiz False

255cm2 255 \, cm^2
GCSE Quiz False

383cm2 383 \, cm^2
GCSE Quiz True

You are calculating the TOTAL surface area of the cylinder, so you find the area of each face and add them together.

 

Lateral surface area=2πrh=2×π×6.1×3.9=149.4769 \begin{aligned}\text{Lateral surface area}&=2\pi rh \\\\ &=2 \times \pi \times 6.1\times 3.9 \\\\ &=149.4769…\\\end{aligned}

 

Area of circle =πr2=π×6.12=116.8986 \begin{aligned}\text{Area of circle }&=\pi r^2 \\\\ &=\pi \times 6.1^2 \\\\ &=116.8986…\end{aligned}
Total surface area: 149.4769+116.8986+116.8986=383.2741 149.4769+116.8986+116.8986=383.2741

 

Surface area (rounded to the nearest whole number) =383 cm2 = 383 \mathrm{~cm}^2

5. Calculate the TOTAL surface area of the cylinder below.

 

Round your answer to the nearest whole number.

 

Surface area of a cylinder 18 US

192cm2 192 \, cm^2
GCSE Quiz True

191cm2 191 \, cm^2
GCSE Quiz False

610cm2 610 \, cm^2
GCSE Quiz False

611cm2 611 \, cm^2
GCSE Quiz False

You are calculating the TOTAL surface area of a cylinder, so you find the area of each face and add them together.

 

Lateral surface area=2πrh=2×π×2.7×8.6=145.8955 \begin{aligned}\text{Lateral surface area}&=2\pi rh \\\\ &=2 \times \pi \times 2.7\times 8.6 \\\\ &=145.8955…\\\end{aligned}

 

Area of circle =πr2=π×2.72=22.9022 \begin{aligned}\text{Area of circle }&=\pi r^2 \\\\ &=\pi \times 2.7^2 \\\\ &=22.9022…\end{aligned}

 

Total surface area: 145.8955+22.9022+22.9022=191.6999 145.8955+22.9022+22.9022=191.6999

 

Surface area (rounded to the nearest whole number) =192 cm2 = 192 \mathrm{~cm}^2

6. Calculate the TOTAL surface area of the cylinder below.

 

Leave your answer in terms of π. \pi .

 

Surface area of a cylinder 19 US

34πcm2 34\pi \, cm^2
GCSE Quiz False

38πcm2 38\pi \, cm^2
GCSE Quiz False

38πcm2 38\pi \, cm^2
GCSE Quiz False

32πcm2 32\pi \, cm^2
GCSE Quiz True

You are calculating the TOTAL surface area of a cylinder, so you find the area of each face and add them together.

 

Lateral surface area=2πrh=2×π×2×6=24π \begin{aligned}\text{Lateral surface area}&=2\pi rh \\\\ &=2 \times \pi \times 2\times 6 \\\\ &=24\pi \\\end{aligned}

 

Area of circle =πr2=π×22=4π \begin{aligned}\text{Area of circle }&=\pi r^2 \\\\ &=\pi \times 2^2 \\\\ &=4 \pi\end{aligned}

 

Total surface area:  24π+4π+4π=32πcm2  24\pi + 4 \pi + 4 \pi = 32\pi \mathrm{cm}^{2}

Surface area of a cylinder FAQs

How is the volume of cylinders different from the total surface area of cylinders?

To find the volume of a cylinder, find the area of the base, a circle and multiply it by the height. You can do this with the formula 2πr2h. 2 \pi r^2 h. The total surface area is found by adding the area of the two bases and the lateral side.

The lateral side is measured by the height of the cylinder and the circumference of the circle. You can use the surface area of a cylinder formula 2πrh+2πr2 2 \pi r h+2 \pi r^2 to solve for any cylinder.

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