# Surface Area

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

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

This is level 2; Use a formula to find the surface area of standard solid shapes. The diagrams are not to scale.

 Find the surface area of a cube if the length of each side is 5.8cm. Give your answer to the nearest square centimetre. cm2 Find the surface area of this cuboid if AB = 25cm, BC = 33cm and CD = 30cm. cm2 Find the surface area of this solid cylinder if the radius of the circular top is 42cm and its height is 45cm. Give your answer to the nearest square centimetre. cm2 Find the surface area of a solid cone if the radius of the circular base is 25cm and the length of the sloping side is 34cm. Give your answer to the nearest square centimetre. cm2 Find the surface area of a sphere with a diameter of 76cm. Give your answer to the nearest square centimetre. cm2 Find the surface area of a triangular prism if the area of its cross section is 10cm2, its length is 41cm and the 3 sides of the triangular ends add up to 15. cm2 Find the surface area of a solid cylinder if the diameter of the circular end is 74cm and its length is 41cm. Give your answer to the nearest square centimetre. cm2 Find the surface area of a square based pyramid if the length of a side of the square base is 6cm and the area of each triangular face is 37cm2. cm2 The cross section of a prism is a right angled triangle as shown in the diagram. Calculate the surface area of the prism if AB = 16cm, BC = 15cm and CD = 20cm. cm2 The cross section of a prism is an 'L-shaped' as shown in the diagram. Calculate the surface area of the prism if AB = 37cm, BC = 37cm, CD = 9cm, DE = 9cm and AF = 12cm. cm2
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## Instructions

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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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