# Surface Area

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

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This is level 6; Find the surface area of a variety of pyramids. The diagrams are not to scale.

 1 Find the surface area of a square based pyramid if the length of a side of thesquare base is 6cm and the area of each triangular face is 52cm2. ☐ cm2 ☐ ✓ ✗ 2 Find the surface area of a square-based pyramid with a height of 17cm and base with sides of length 16cm. Give your answer to the nearest square centimetre. ☐ cm2 ☐ ✓ ✗ 3 Find the surface area of a square-based pyramid with a height of 32cm and base with an area of 1296cm2. Give your answer to the nearest square centimetre. ☐ cm2 ☐ ✓ ✗ 4 Find the surface area of this rectangular-based pyramid. Give your answer to the nearest square centimetre. ☐ cm2 ☐ ✓ ✗ 5 A square-based right pyramid is made from the net shown below.Calculate the surface area of the pyramid. ☐ cm2 ☐ ✓ ✗ 6 The pyramids in Egypt are huge! Blocks of white limestone from quarries across the Nile were used to cover the pyramid's four triangular faces. Imagine that you were the official and only pyramid polisher? How many days would it take you to polish one pyramid (base side 100m, height 144m) working at the rate of 5 minutes per square metre and working eight hours per day. Round your answer up to the next whole number of days. ☐ cm2 ☐ ✓ ✗
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This is Surface Area level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7 Level 8 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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