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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

1.73m

4. The length of the cylinder above is 1.73m. 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

4.62cm

6. The height of the cylinder above is 4.62cm. Find its radius if its surface area is 154cm2.

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
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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.

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Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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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:

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Description of Levels

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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.

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Curriculum Reference

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

Cylinder Formulae

This video is from the talented Dr Frost

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.

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