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SubstitutionPerimeter

Areas of circlesArea of compound shapes

Applying formulae to calculate and solve problems involving

Area of quadrilaterals Rounding numbersThis topic is relevant for:

Here we will learn about the volume of a cylinder, including how to calculate the volume of a cylinder given its radius and perpendicular height.

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

The **volume of a cylinder **is the amount of space there is inside a cylinder.

In order to find the volume of a cylinder we first need to find the circular area of the base.

The formula for calculating the area of a circle is:

\text{Area}=\pi r^2We then multiply the area of the circular base by the height (or length) of the cylinder.

The **formula for the volume of a cylinder** is:

Where r ** is the radius** of a cylinder and h is the **perpendicular height** of a cylinder.

E.g.

Find the volume of this cylinder with radius of the base 7 cm and perpendicular height 10 cm .

\[\text{Volume}=\pi r^2 h\\
=\pi \times 7^2 \times 10\\
=490\pi\\
=1539.380…\\
=1539.4 \ cm^3 \ \text{(to 1 dp)}\\\]

In order to calculate the volume of a cylinder:

**Write down the formula:**\text{Volume}=\pi r^2 h**Substitute the given values.****Work out the calculation.****Write the final answer, including units.**

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

COMING SOONGet your free volume of a cylinder worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONFind the volume of the cylinder with radius 3 cm and perpendicular height 5 cm .

Give your answer to 1 decimal place.

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h2**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

V=\pi \times 3^2 \times 53**Work out the calculation.**

Use a calculator to work out the volume.

V=45\pi = 141.371…4**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding. Here we are asked to give the answer to 1 decimal place.

V=141.371…=141.4 cm^3 \ \text{(to 1 dp)}The volume of the cylinder is: 141.4 cm^{3} (to 1 dp)

Find the volume of the cylinder with radius 4.8 cm and perpendicular height 7.9 cm .

Give your answer to 3 significant figures.

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

V=\pi \times 4.8^2 \times 7.9**Work out the calculation.**

Use a calculator to work out the volume.

V= 571.820…**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 3 significant figures.

V=571.820…=572 cm^3 \ \text{(to 3 sf)}The volume of the cylinder is: 572 cm^{3} (to 3 sf)

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

Leave your answer in terms of \pi .

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

V=\pi \times 3^2 \times 7**Work out the calculation.**

Work out the volume (focusing on the number parts of the calculation).

V= 63\pi**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 3 significant figures.

V=63\pi=63\pi cm^3The volume of the cylinder is: 63 cm^{3}

Find the volume of the cylinder with radius 4 cm and perpendicular height 10 cm .

Leave your answer in terms of \pi .

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

V=\pi \times 4^2 \times 10**Work out the calculation.**

Work out the volume (focusing on the number parts of the calculation).

V= 160\pi**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 3 significant figures.

V=160\pi =160\pi cm^3The volume of the cylinder is: 160 cm^{3}

The volume of a cylinder is 1600 cm^{3} .

Its radius is 9 cm .

Find its perpendicular height.

Give your answer to 2 decimal places.

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

1600=\pi \times 9^2 \times h**Work out the calculation.**

We need to rearrange the formula to find the value of h .

\[1600= \pi \times 81 \times h\\
\frac{1600}{\pi \times 81}=h\\
h=6.287…\\\]

**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 2 decimal places.

h = 6.287... = 6.29 \ cm \ \text{(to 2 dp)}The perpendicular height of the cylinder is: 6.29 cm (to 2 dp)

The volume of a cylinder is 1400 cm^{3} .

Its perpendicular height is 15 cm .

Find its radius.

Give your answer to 2 decimal places.

**Write down the formula.**

To answer the question we need the formula for the volume of a cylinder.

\text{Volume}=\pi r^2 h**Substitute the given values.**

We need to substitute the value of the radius r and the perpendicular height h into the formula.

1400=\pi \times r^2 \times 15**Work out the calculation.**

We need to rearrange the formula to find the value of h .

\[1400=\pi \times r^2 \times 15\\
\frac{1400}{\pi \times 15}=r^2\\
r^2=29.70892…\\
r=\sqrt{29.70892…}\\\]

**Write the final answer, including units.**

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 2 decimal places.

r=\sqrt{29.70892…} =5.4505... = 5.45 \ cm \ \text{(to 2 dp)}The radius of the cylinder is: 5.45 cm (to 2 dp)

**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.

**Correc**t units

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

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

Volume of a cylinder is part of our series of lessons to support revision on rounding numbers. You may find it helpful to start with the main cylinder lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Find the volume of a cylinder with a radius 3.2 cm and perpendicular height 9.1 cm.

Give your answer to 3 significant figures.

293 cm^3

292 cm^3

832 cm^3

833 cm^3

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

V=\pi r^2 h\\ V=\pi \times 3.2^2 \times 9.1\\ V=292.746…\\ V=293 \ cm^3 \ \text{(to 3 sf)}\\2. Find the volume of a cylinder with a radius 5.3 cm and perpendicular height 3.8 cm .

Give your answer to 3 significant figures.

336 cm^3

240 cm^3

241 cm^3

335 cm^3

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

V=\pi r^2 h\\ V=\pi \times 5.3^2 \times 3.8\\ V=335.339…\\ V=335 \ cm^3 \ \text{(to 3 sf)}\\3. Find the volume of a cylinder with a radius 8 cm and perpendicular height 7 cm .

Leave your answer in terms of \pi .

446\pi cm^3

444\pi cm^3

448\pi cm^3

442\pi cm^3

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

V=\pi r^2 h\\ V=\pi \times 8^2 \times 7\\ V=448\pi\\ V=448\pi \ cm^3\\4. Find the volume of a cylinder with a radius 4 cm and perpendicular height 8 cm .

Give your answer to 3 significant figures.

335 cm^3

336 cm^3

240 cm^3

241 cm^3

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

V=\pi r^2 h\\ V=\pi \times 4^2 \times 8\\ V=128\pi\\ V=128\pi \ cm^3\\5. The volume of a cylinder is 250 cm^3 .

Its radius is 2.9 cm .

Find its perpendicular height.

Give your answer to 2 decimal places.

9.43 cm

9.46 cm

9.44 cm

9.45 cm

Using the formula we substitute the value of the volume and the value of the radius and rearrange to find the radius.

V=\pi r^2 h\\ 250=\pi \times 2.9^2 \times h\\ \frac{250}{\pi \times 2.9^2}=h\\ h=9.4622…\\ h=9.46 \ cm \ \text{(to 2 dp)}\\6. The volume of a cone is 800 cm^3 .

Its perpendicular height is 9.2 cm .

Find its radius.

Give your answer to 2 decimal places.

5.26 cm

5.24 cm

5.25 cm

5.27 cm

Using the formula we substitute the value of the volume and the value of the perpendicular height and rearrange to find the radius.

V=8 \pi r^2 h\\ 800=8\pi \times r^2 \times 9.2\\ 800=\pi \times r^2 \times 9.2\\ \frac{800}{\pi \times 9.2}=r^2\\ r=\sqrt{\frac{800}{\pi \times 9.2}}\\ r=5.2610…\\ r=5.26 \ cm \ \text{(to 2 dp)}\\1. Here is a cylinder.

Calculate the volume of the cylinder.

Give your answer to 3 significant figures.

**(2 marks)**

Show answer

\pi \times 5.3^2 \times 4.7

For substituting the radius and the perpendicular height into the formula

**(1)**

414.762…=415

For the correct answer

**(1)**

2. Here is a cylinder.

Calculate the volume of the cylinder.

Leave your answer in terms of \pi .

**(2 marks)**

Show answer

\pi \times 3^2 \times 8

For substituting the radius and the perpendicular height into the formula

**(1)**

72\pi

For the correct answer

**(1)**

3. This diagram shows a container.

The container is in the shape of a cylinder.

The container is empty.

Nina has a bucket.

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

The bucket holds 8 litres of water.

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

( 1 litre = 1000 cm^2 )

**(4 marks)**

Show answer

\pi \times 25^2 \times 80

For using the formula to find the volume of the container

**(1)**

157 079.63…

For the correct volume

**(1)**

157 079.63… \div 8000

For dividing the volume of the container by the volume of the buckets with the same units

**(1)**

=19.63… = 20 buckets

For the correct number of buckets

**(1)**

You have now learned how to:

- Work out the volume of a cylinder
- Solve problems involving the volume of a cylinder

- Volume of a cone
- Surface area of a cone
- Volume of a sphere
- Surface area of a sphere

For GCSE we look at right circular cylinders – where the bases are parallel planes and the height is perpendicular to these bases. It is possible to have oblique cylinders.

It is also possible to have a cylinder with an ellipse as its cross-section.

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