Transum Software

Surface Area

Calculate the surface areas of the given basic solid shapes using standard formulae.
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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 6cm and a base radius of 4.9cm 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 19cm and the
length of the sloping side is 46cm. 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 28cm.
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 23cm. 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.

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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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