Transum Software

Surface Area

Calculate the surface areas of the given basic solid shapes using standard formulae.

Level 1 Level 2 Level 3 Level 4 Volume Exam-Style Description Help More

This is level 4; Use a formula to find the surface area of standard solid shapes. The diagrams are not to scale.

Shape1 1. Find the surface area of this solid cylinder if the radius of the circular top is 42cm and its height is 39cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape2 2. Find the surface area of a solid cone if the radius of the circular base is 25cm and the length of the sloping side is 34cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape3 3. Find the surface area of a sphere with a diameter of 90cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape4 4. Find the surface area of a triangular prism if the area of its cross section is 83cm2, its length is 37cm and the 3 sides of the triangular ends add up to 42. cm2 Correct Wrong
Shape5 5. Find the surface area of a solid cylinder if the diameter of the circular end is 84cm and its length is 45cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape6 6. Find the surface area of a square based pyramid if the length of a side of the square base is 10cm and the area of each triangular face is 45cm2. cm2 Correct Wrong
Shape7 7. The cross section of a prism is a right angled triangle as shown in the diagram. Calculate the surface area of the prism if AB = 8cm, BC = 12cm and CD = 16cm. cm2 Correct Wrong
Shape8 8. A cylindrical tube is used to store circular salted potatoe crisps. All if its external surface area except one of the circular ends is painted red. Calculate the area of the painted region if the length of the tube is 32cm and the diameter of the tube is 11cm. Give your answer to the nearest square centimetre.

cm2 Correct Wrong
Shape9 9. A sphere has a surface area of 100cm2. Calculate its radius in centimetres giving your answer to three significant figures. cm2 Correct Wrong
Shape10 10. The frame for a large tent is in the shape of an isosceles triangular prism. The height of the tent is 2.6m, the width of the tent (at the triangular ends) is 3.1m, the sloping edges of the tent are each 3.02m an the length of the tent is 4.7m. Calculate the area of canvas needed for the tent (excluding the bottom of the prism as that is where the ground sheet goes). Give your answer to the nearest integer.

cm2 Correct Wrong


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.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

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 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK:

"I am an NQT and have only just discovered this website. I nearly wet my pants with joy.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School:

"This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register."

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

Tran Tunnels

Tran Tunnels

Answer the questions as you find your way through the tunnels. Collect coins on the way. There's a musical theme to this adventure game and you won't be able to complete it unless you solve all of the clues.


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:


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.


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:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2020 WWW.TRANSUM.ORG

Description of Levels



Level 1 - Find the surface area of shapes made up of cubes.

Level 2 - Find the surface area of a variety of cuboids.

Level 3 - Find the surface area of cuboids and other composite shapes.

Level 4 - Use a formula to find the surface area of standard solid shapes.

Volume - Find the volume of basic solid shapes.

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

Surface Area Formulae

Cube: \(6s^2\) where \(s\) is the length of one edge.

Cuboid: \(2(lw + lh + wh)\) where \(l\) is the length, \(w\) is the width and \(h\) is the height of the cuboid.

Cylinder: \(2\pi rh + 2\pi r^2\) where \(h\) is the height (or length) of the cylinder and \(r\) is the radius of the circular end.

Cone: \(\pi r(r+l)\) where \(l\) is the distance from the apex to the rim of the circle (sloping height) of the cone and \(r\) is the radius of the circular base.

Cone: \(\pi r(r+\sqrt{h^2+r^2})\) where \(h\) is the height of the cone and \(r\) is the radius of the circular base.

Square based pyramid: \(s^2+2s\sqrt{\frac{s^2}{4}+h^2}\) where \(h\) is the height of the pyramid and s is the length of a side of the square base.

Sphere: \(4\pi r^2\) where \(r\) is the radius of the sphere.

Prism: Double the area of the cross section added to the product of the length and the perimeter of the cross section.

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.