Surface AreaCalculate the surface areas of the given basic solid shapes using standard formulae. 
This is level 9; Mixed, more challenging questions involving surface area. The diagrams are not to scale.
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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/Alevel exam paper questions (worked solutions are available for Transum subscribers).
More on 3D Shapes including lesson Starters, visual aids, investigations and selfmarking exercises.
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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