Transum Software

Surface Area

Calculate the surface areas of the given basic solid shapes using standard formulae.
Menu Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Exam Help

This is level 5; Find the surface area of a variety of cones. The diagrams are not to scale.

1

A right cone is a cone with its vertex above the center of its base.
Calculate the surface area of this right cone with a sloping height of 5.8cm and a base radius of 3.8cm giving your answer in square centimetres to three significant figures.

Shape 1

☐ cm2 ☐ ✓ ✗

2

Calculate the surface area of this right cone with a height of 4.5cm and a base radius of 3.7cm giving your answer in square centimetres to three significant figures.

Shape 2

☐ cm2 ☐ ✓ ✗

3

Find the surface area of a solid cone if the radius of the circular base is 10cm and the
length of the sloping side is 47cm. Give your answer to the nearest square centimetre.

Shape 3

☐ cm2 ☐ ✓ ✗

4

Calculate the surface area of a right cone with a diameter of 28.2cm, a radius of 14.1cm, a height of 16.2cm and a sloping height of 21.5cm. Give your answer in square centimetres to three significant figures.

Shape 4

☐ cm2 ☐ ✓ ✗

5

Calculate the surface area of a cone with diameter and sloping side both equal to 40cm.
Give your answer in square centimetres to three significant figures.

☐ cm2 ☐ ✓ ✗

6

Calculate the curved surface area only of a cone with diameter and height both
equal to 26cm. Give your answer in square centimetres to three significant figures.

☐ cm2 ☐ ✓ ✗

Check

This is Surface Area level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6 Level 7 Level 8 Level 9

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 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

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

Polygon Pieces

Polygon Pieces

Arrange the nine pieces of the puzzle on the grid to make the given polygon. Level one is for those learning the names of shapes while other levels are for those who like a challenge!

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!

For Students:

 

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program
©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=264

Description of Levels

Close

❎

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 a variety of prisms.

Level 4 - Find the surface area of a variety of cylinders.

Level 5 - Find the surface area of a variety of cones.

Level 6 - Find the surface area of a variety of pyramids.

Level 7 - Find the surface area of a variety of spheres.

Level 8 - Find the surface area of composite shapes.

Level 9 - Mixed, more challenging questions involving surface area.

Volume - Find the volume of basic solid shapes.

Surface Area = Volume - Can you find the ten cuboids that have numerically equal volumes and surface areas? A challenge in using technology.

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 3D Shapes 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

Help Video

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.

Rectangular based pyramid: \(lw+l\sqrt{\frac{w^2}{4}+h^2}+w\sqrt{\frac{l^2}{4}+h^2}\) where \(h\) is the height of the pyramid, \(l\) is the length of the base and \(w\) is the width of the 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.

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

❎