Transum Software

Cylinders

Apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions

Level 1 Level 2 Level 3 Exam-Style Description Help More 3D Shapes

This is level 3: mixed questions requiring the formulae for the volumes and surface areas of cylinders. You can earn a trophy if you get at least 6 questions correct and you do this activity online. The diagrams are not to scale. All answers should be given to three significant figures.

Glass ofCherry Juice

1. Though it does not look look very cylindrical in the photograph due to perspective, the glass is a cylinder. 200ml of cherry juice has been poured into the glass. The diameter of the glass is 7.8cm. How deep is the juice in the glass? [1ml = 1 cm3]

cm Correct Wrong

2. The length of a cylindrical pipe is exactly 33 times its diameter. If the volume of the pipe is 23 litres calculate the pipe's diameter. [1 litre = 1000 cm3]

cm Correct Wrong

3. A gold cylinder with a radius of 5cm and length 22.3cm is melted down then all of the gold is used to make a new cylinder with radius 10cm. Calculate the length of the new cylinder.

cm Correct Wrong

2.12m

4. The length of the cylinder above is 2.12m. Calculate the cylinder's capacity in litres [1 litre = 1000 cm3] given that its radius is 65% of its length.

l Correct Wrong

5. The surface area of a cylinder is 100m2 and its length is twice its radius. Find the diameter of the cylinder in metres.

m Correct Wrong

4.84cm

6. The height of the cylinder above is 4.84cm. Find its radius if its surface area is 108cm2.

cm Correct Wrong

Baked Beans

7. Forty eight tins of baked beans are packed tightly together in a cardboard box. There are two layers of tins and each layer is arranged in a four by six rectangle. If the height of a tin is three times the radius and the volume of the box is 36.864 litres, calculate the capacity of one tin in cubic centimetres.

cm3 Correct Wrong

Gas Holder

8. The photograph shows the 30,000m3 blast furnace gas holder at Rautaruukki Steel in Finland. It is a cylider and its height 10% longer than its diameter. It is time for the top and curved walls to be painted on the outside. Calculate the cost of repainting the gas holder if a 5 litre tin of paint costs £25 and covers 60 m2. [Note that only whole tins of paint can be purchased so your answer should be a multiple of 25.]

£ Correct Wrong
Check

This is Cylinders level 3. You can also try:
Level 1 Level 2

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Nim

Nim

A very old game but one which involves mathematical based strategies. Take turns with the computer to remove items from the piles. You can remove as many items from the same row as you like. Whoever removes the last item is the winner.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Transum.org is a proud supporter of the kidSAFE Seal Program

© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=772

Description of Levels

Close

Close

Level 1 - Applying the formula for the volume of a cylinder

The numbers used in the questions in level 1 are randomly generated. This means you will get a different set of questions each time the page is loaded.

Level 2 - Applying the formula for the surface area of a cylinder

The numbers used in the questions in level 2 are randomly generated. This means you will get a different set of questions each time the page is loaded.

Level 3 - Mixed questions requiring the formulae for the volumes and surface areas of cylinders

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Cylinder Formulae

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Close

Close