Cylinder

Here we will learn about cylinders, including how to find the volume of a cylinder.  We will also learn about how to find the curved surface area of a cylinder and its total surface area.

There are also cylinder worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a cylinder?

A cylinder is a three dimensional object that has two flat ends which are circles and one curved side.  It has a circular cross-section which is the same all the way through the shape.

The radius of the circle is r r and the perpendicular height of the cylinder is h h .

Cylinder Image 1

The cylinders that will feature in GCSE Mathematics are known as right cylinders or right circular cylinders but actually a cylinder can have elliptical ends rather than circular ends. The end shapes just need to be closed curved shapes that lie in parallel planes. It can also have a curved side which is not perpendicular to the base. These are known as oblique cylinders.

What is a cylinder?

What is a cylinder?

Volume of a cylinder

The volume of a cylinder is how much space there is inside a cylinder. t can be found by multiplying the height of a cylinder by the area of its base.

The formula for the volume of a cylinder is:

Volume=πr2h \text{Volume}=\pi r^2 h

E.g. Find the volume of the cylinder

Cylinder Image 2

Volume=πr2h=π×42×10=160π=502.7 cm3 (to 1 dp) \begin{aligned} \text{Volume}&=\pi r^2 h\\\\ &=\pi \times 4^2 \times 10\\\\ &=160\pi\\\\ &=502.7 \ cm^3 \ \text{(to 1 dp)} \end{aligned}

Step-by-step guide: Volume of a cylinder

How to calculate the volume of a cylinder

In order to calculate the volume of a cylinder:

  1. Write down the formula.
  2. Substitute the given values.
  3. Work out the calculation.
  4. Write the final answer, including units.

How to calculate the volume of a cylinder

How to calculate the volume of a cylinder

Cylinder worksheet

Cylinder worksheet

Cylinder worksheet

Get your free cylinder worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Cylinder worksheet

Cylinder worksheet

Cylinder worksheet

Get your free cylinder worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Volume of a cylinder examples

Example 1: volume of a cylinder

Find the volume of the cylinder with radius 3.8  cm 3.8 \; cm and perpendicular height 6.1  cm. 6.1 \; cm.

Give your answer to 1 1 decimal place.

Cylinder Example 1

  1. Write down the formula.

 Volume =πr2h \text { Volume } =\pi r^{2} h

2Substitute the given values.

 Volume =πr2h=π×3.82×6.1 \begin{aligned} \text { Volume } &=\pi r^{2} h \\\\ &=\pi \times 3.8^{2} \times 6.1 \end{aligned}

3Work out the calculation.

=π×3.82×6.1=276.724 \begin{aligned} &=\pi \times 3.8^{2} \times 6.1 \\\\ &=276.724 \ldots \end{aligned}

4Write the final answer, including units.

=276.7 cm3( to 1.d.p) =276.7 \mathrm{~cm}^{3}(\text { to } 1 . d . p)

Example 2: volume of a cylinder

Find the volume of the cylinder with radius 3 cm 3 \ cm and perpendicular height 7 cm. 7 \ cm.

Leave your answer in terms of π. \pi.

Cylinder Example 2

Write down the formula.

Show step

Substitute the given values.

Show step

Work out the calculation.

Show step

Write the final answer, including units.

Show step

Surface area of a cylinder

The surface area of a cylinder is the area which covers the outer surface of a cylinder. The surface area of a cylinder is made up of three parts, a curved surface area and two circular bases.

Cylinder Image 3

The formula for calculating the curved surface area of a cylinder is:

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

The formula for calculating the area of a circle:

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

For the total surface area, we can add the curved surface area to the area of the two circles:

total surface area=2πrh+2πr2 \text{total surface area}=2\pi rh+2\pi r^2

E.g. Find the surface area of cylinder

Cylinder Image 2

Curved surface area=2πrh=2×π×4×10=80π \text{Curved surface area}=2\pi rh=2\times \pi \times 4 \times 10=80\pi

Area of a circle=πr2=π×42=16π \text{Area of a circle}=\pi r^2=\pi \times 4^2=16\pi

total surface area=80π+2×16π=80π+32π=112π=315.9 cm2 (to 1 dp) \begin{aligned} \text{total surface area}&=80\pi +2\times 16\pi \\\\ &=80\pi+32\pi\\\\ &=112\pi\\\\ &=315.9 \ cm^2 \ \text{(to 1 dp)} \end{aligned}

Step-by-step guide: Surface area of a cylinder

How to calculate the surface area of a cylinder

In order to calculate the surface area of a cylinder:

  1. Work out the area of each face.
  2. Add the areas together.
  3. Include units.

How to calculate the surface area of a cylinder

How to calculate the surface area of a cylinder

Surface area of a cylinder examples

Example 3: total surface area of a cylinder

Find the total surface area of the cylinder with radius 7.8  cm 7.8 \; cm and perpendicular height 6.5  cm. 6.5 \; cm.

Give your answer to 1 1 decimal place.

Cylinder Example 3

Work out the area of each face.

Show step

Add the areas together.

Show step

Include units.

Show step

Example 4: total surface area of a cylinder

Find the curved surface area of the cylinder with radius 5  cm 5 \; cm and perpendicular height 9  cm. 9 \; cm.

Leave your answer in terms of π. \pi.

Cylinder Example 4

Work out the area of each face.

Show step

Add the areas together.

Show step

Include units.

Show step

Common misconceptions

  • Using the correct formula

There are several formulas that can be used, so we need to match the correct formula to the correct context

  • Rounding

It is important to not round the answer until the end of the calculation. This will mean your final answer is accurate.

  • Using 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.

  • Make sure you have the correct units

For area we use square units such as cm2 cm^2 .

For volume we use cube units such as cm3. cm^3.

Did you know…

The name cylinder gets used a lot for objects in real life such as hydraulic cylinders, gas cylinders or hot water cylinders used in heating systems. Not all of these are true cylinders but compound shapes involving hollow cylinders and hemispheres.

Practice cylinder questions

1. Find the volume of a cylinder of radius 2.9  cm 2.9 \; cm and perpendicular height 5.7  cm. 5.7 \; cm.

 

Give your answer to 3 3 significant figures.

 

Cylinder Practice Question 1

 

150  cm3 150 \; cm^3
GCSE Quiz False

151  cm3 151 \; cm^3
GCSE Quiz True

296  cm3 296 \; cm^3
GCSE Quiz False

297  cm3 297 \; cm^3
GCSE Quiz False

We are finding the volume of a cylinder so we substitute the value of r r and h h into the formula.

 

V=πr2hV=\pi r^2 h
V=π×2.92×5.7V=\pi \times 2.9^2 \times 5.7
V=150.598V=150.598…
V=151 cm3 (to 3 sf)V=151 \ cm^3 \ \text{(to 3 sf)}

2. Find the volume of a cylinder of radius 3  cm 3 \; cm and perpendicular height 10  cm. 10 \; cm.

 

Leave your answer in terms of π \pi .

 

Cylinder Practice Question 2

92π  cm3 92\pi \; cm^3
GCSE Quiz False

94π  cm3 94\pi \; cm^3
GCSE Quiz False

90π  cm3 90\pi \; cm^3
GCSE Quiz True

96π  cm3 96\pi \; cm^3
GCSE Quiz False

We are finding the volume of a cylinder so we substitute the value of r r and h h into the formula.

 

V=πr2hV=\pi r^2 h
V=π×32×10V=\pi \times 3^2 \times 10
V=90πV=90\pi
V=90π cm3V=90\pi \ cm^3

3. Find the curved surface area of a cylinder of radius 9.5  cm 9.5 \; cm and perpendicular height 7.2  cm. 7.2 \; cm.

 

Give your answer to 3 3 significant figures.

 

Cylinder Practice Question 3

430  cm2 430 \; cm^2
GCSE Quiz True

428  cm2 428 \; cm^2
GCSE Quiz False

429  cm2 429 \; cm^2
GCSE Quiz False

427  cm2 427 \; cm^2
GCSE Quiz False

We are finding the curved surface area of a cylinder so we substitute the value of r r and h h into the formula.

 

Curved surface area =2πrh =2\pi rh
=2×π×9.5×7.2 =2 \times \pi \times 9.5\times 7.2
=429.769 =429.769…
=430 cm2to3sf =430 \ cm^2 to 3 sf

4. Find the curved surface area of a cylinder of radius 4  cm 4 \; cm and perpendicular height 6  cm. 6 \; cm.

 

Leave your answer in terms of π \pi .

 

Cylinder Practice Question 4

42π  cm3 42\pi \; cm^3
GCSE Quiz False

44π  cm3 44\pi \; cm^3
GCSE Quiz False

46π  cm3 46\pi \; cm^3
GCSE Quiz False

48π  cm3 48\pi \; cm^3
GCSE Quiz True

We are finding the curved surface area of a cylinder so we substitute the value of r r and h h into the formula.

 

Curved surface area =2πrh =2\pi rh
=2×π×4×6 =2 \times \pi \times 4\times 6
=48π =48\pi
=48π cm2 =48\pi \ cm^2

5. Find the total surface area of a cylinder of radius 4.2  cm 4.2 \; cm and perpendicular height 9.8  cm. 9.8 \; cm.

 

Give your answer to 3 3 significant figures.

 

Cylinder Practice Question 5

 

370  cm2 370 \; cm^2
GCSE Quiz False

862  cm2 862 \; cm^2
GCSE Quiz False

369  cm2 369 \; cm^2
GCSE Quiz True

863  cm2 863 \; cm^2
GCSE Quiz False

We are finding the total surface area of a cylinder so we need to find the area of each face and add them together.

 

Curved surface area =2πrh =2\pi rh
=2×π×4.2×9.8 =2 \times \pi \times 4.2\times 9.8
=258.6159 =258.6159…

 

Area of circle =πr2 =\pi r^2
=π×4.22 =\pi \times 4.2^2
=55.4176 =55.4176…

6. Find the total surface area of a cylinder of radius 8  cm 8 \; cm and perpendicular height 5  cm. 5 \; cm.

 

Leave your answer in terms of π \pi .

 

Cylinder Practice Question 6

144π  cm3 144\pi \; cm^3
GCSE Quiz False

208π  cm3 208\pi \; cm^3
GCSE Quiz True

105π  cm3 105\pi \; cm^3
GCSE Quiz False

130π  cm3 130\pi \; cm^3
GCSE Quiz False

We are finding the total surface area of a cylinder so we need to find the area of each face and add them together.

 

Curved surface area =2πrh =2\pi rh
=2×π×8×5 =2 \times \pi \times 8\times 5
=80π =80\pi

 

Area of circle =πr2 =\pi r^2
=π×82 =\pi \times 8^2
=64π =64 \pi

 

Total surface area: 80π+64π+64π=208π 80\pi + 64 \pi + 64 \pi = 208\pi

Cylinder GCSE questions

1. Here is a cylinder.

 

Cylinder GCSE Question 1

 

Calculate the volume of the cylinder.

Give your answer to 3 3 significant figures.

 

(2 marks)

Show answer
π×3.52×8.7 \pi \times 3.5^2 \times 8.7

(1)

334.815=335 334.815…=335

(1)

2. Here is a cylinder.

 

Cylinder GCSE Question 2

 

Calculate the total surface area of the cylinder.

Leave your answer in terms of π \pi .

 

(3 marks)

Show answer
2×π×9×6=108π 2\times \pi \times 9 \times 6=108\pi

(1)

108π+2×π×92=108π+162π 108\pi + 2\times \pi \times 9^2=108\pi+162\pi

(1)

270π 270\pi

(1)

3. This diagram shows a container.

 

Cylinder GCSE Question 3

 

The container is in the shape of a cylinder.

The container is empty.

 

Tom has a bucket

He is going to use the bucket to fill the container with water.

 

The bucket holds 12 12 litres of water.

How many buckets of water are needed to fill the container?

 

(1 1 litre =1000  cm3 = 1000 \; cm^3 )

 

(4 marks)

Show answer
π×552×35 \pi \times 55^2 \times 35

(1)

332616.12 332 616.12…

(1)

332616.12÷12000 332 616.12… \div 12 000

(1)

=27.718=28 =27.718… = 28 buckets

(1)

Learning checklist

You have now learned how to:

  • Calculate the volume of a cylinder
  • Calculate the curved surface area of a cylinder 
  • Calculate the total surface area of a cylinder 

The next lessons are

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