Surface AreaCalculate the surface areas of the given basic solid shapes using standard formulae. 
This is level 7; Find the surface area of a variety of spheres. The diagrams are not to scale.
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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." 
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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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