# Surface Area

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

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

This is level 3; Find the surface area of cuboids and other composite shapes. The diagrams are not to scale.

 1. What is the surface area of a cuboid shaped box of length 34.5cm, width 30cm and height 40cm? cm2 2. Find the surface area of a cube if the length of each side is 15.5cm. Give your answer to the nearest square centimetre. cm2 3. Find the surface area of this cuboid if AB = 31cm, BC = 35cm and CD = 29cm. cm2 4. Calculate the total surface area of this shape in square centimetres. cm2 5. Calculate the total surface area of this shape in square centimetres. cm2 6. A lump of clay is in the shape of a cuboid with dimensions 12cm, 17cm and 25cm. 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 7. 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 = 8cm, DE = 12cm and AF = 14cm. cm2 8. Find the surface area of a cube if the length of all the edges added together is 171.6cm. Give your answer to the nearest square centimetre. cm2
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#### Polygon Pieces

Arrange the nine pieces of the puzzle on the grid to make the given polygon. Level one is for those learning the names of shapes while other levels are for those who like a challenge!

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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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