Transum Software

Surface Area

Calculate the surface areas of the given basic solid shapes using standard formulae.
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This is level 4; Find the surface area of a variety of cylinders. The diagrams are not to scale.

1

Find the surface area of this solid cylinder if the radius of the circular top is 43cm and its height is 42cm. Give your answer to the nearest square centimetre.

Shape

☐ cm2 ☐ ✓ ✗

2

Find the surface area of a solid cylinder if the diameter of the circular end is 72cm and its length is 37cm. Give your answer to the nearest square centimetre.

Shape

☐ cm2 ☐ ✓ ✗

3

Find the surface area of this cylinder.
Give your answer to three significant figures.

Shape

☐ cm2 ☐ ✓ ✗

4

A cylindrical tube is used to store circular salted potatoe crisps. All of 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 7cm. Give your answer to the nearest square centimetre.

Shape

☐ cm2 ☐ ✓ ✗

5

A lumberjack needed to calculate the surface area of a log. He estimated that the log was a cylinder with a length of 12 metres and diameter 70 centimetres.
What did he calculate the surface area to be? Give your answer to the nearest square metre.

Shape

☐ cm2 ☐ ✓ ✗

6

A cylindrical telegraph pole was ten times as tall as it was wide.
Calculate the curved surface area of the pole if it's radius was 30cm. Give your answer in square metres to nearest square metre.

☐ cm2 ☐ ✓ ✗

Check

This is Surface Area level 4. You can also try:
Level 1 Level 2 Level 3 Level 5 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.
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Description of Levels

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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.

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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.

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