# Surface Area

## Calculate the surface area of the given solid shapes.

##### Level 1Level 2Level 3FormulasVolumeDescriptionMore 3D

This is level 1; Find the surface area of simple compound shapes. The diagrams are not to scale.

 Each of the yellow cubes in the diagram have edges 1cm long. What is the total surface area of the cuboid they are part of? cm2 Each of the yellow cubes in the diagram have edges 1cm long. What is the total surface area of the shape they are part of? cm2 Each of the yellow cubes in the diagram have edges 1cm long. What is the total surface area of the shape they are part of? cm2 Each of the yellow cubes in the diagram have edges 1cm long. What is the total surface area of the shape they are part of? cm2 Each of the cubes in the diagram have edges 2cm long. What is the total surface area of the shape they are part of? cm2 Each of the cubes in the diagram have edges 3cm long. What is the total surface area of the shape they are part of? cm2 What is the surface area of a cuboid of length 10cm, width 7cm and height 6cm? cm2 Calculate the total surface area of this shape in square centimetres. cm2 Calculate the total surface area of this shape in square centimetres. cm2 A lump of clay is in the shape of a cuboid with dimensions 10cm, 16cm and 24cm. 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
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## Description of Levels

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Level 1 - Find the surface area of simple compound shapes.

Level 2 - Use a formula to find the surface area of standard solid shapes.

Level 3 - Exam-type questions on mensuration.

You could also try the Volume exercise.

## Volume Formulas

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: $$\pi r(r+\sqrt{h^2+r^2})$$ 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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