# Surface Area

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

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This is level 8; Find the surface area of composite shapes. The diagrams are not to scale.

 1 Calculate the total surface area of this shape in square centimetres. ☐ cm2 ☐ ✓ ✗ 2 Calculate the total surface area of this shape in square centimetres. ☐ cm2 ☐ ✓ ✗ 3 A lump of clay is in the shape of a cuboid with dimensions 9cm, 15cm and 20cm. A cube shaped piece of clay is removed from one of the corners as shown. What is the surface area of the shape that remains? ☐ cm2 ☐ ✓ ✗ 4 The cross section of a prism is an 'L-shaped' as shown in the diagram. Calculate the surface area of the prism if AB = 39cm, BC = 35cm, CD = 15cm, DE = 5cm and AF = 10cm. ☐ cm2 ☐ ✓ ✗ 5 Find the surface area of this rocket shape made up of a cone rising out of a cylinder with measurements given in the diagram. Give your answer to three significant figures. ☐ cm2 ☐ ✓ ✗ 6 A hole of diameter 2cm is drilled through the length of a cuboid as shown in the diagram.Find the total surface area of the composite shape produced. Give your answer to three significant figures. ☐ cm2 ☐ ✓ ✗
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This is Surface Area level 8. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 9

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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.

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## 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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