# Surface Area

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

##### Level 1Level 2Level 3Level 4VolumeExam-StyleDescriptionHelpMore

This is level 2; Find the surface area of a variety of cuboids. The diagrams are not to scale.

 1. What is the surface area of this cuboid with dimensions 6cm, 8cm and 3cm? cm2 2. What is the surface area of this cuboid with dimensions 14cm, 9cm and 12cm? cm2 3. What is the surface area of this cuboid with dimensions 4.1cm, 13cm and 3cm? cm2 4. What is the surface area of this cuboid with dimensions 16cm, 18cm and 9cm? cm2 5. What is the surface area of this cuboid with dimensions 21cm, 26cm and 10cm? cm2 6. What is the surface area of this cuboid with dimensions 1.9cm, 5.2cm and 2.1cm? cm2 7. What is the surface area of this cuboid with dimensions 6.6cm, 8.2cm and 3cm? cm2 8. What is the surface area of this cuboid with dimensions 88cm, 28cm and 30cm? cm2
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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 cuboids and other composite shapes.

Level 4 - Use a formula to find the surface area of standard solid shapes.

Volume - Find the volume of basic solid shapes.

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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.

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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