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Coursework Notes - Shape & Space

 

Volume

 

cuboid

prism

sphere

pyramid

cone

frustrum

 

 

Cuboid - The volume(capacity) of a cuboid is given by:

 

 

cuboid

 

 

note: the sides of a cuboid are at right angles to eachother

 

 

 

Prism - a shape with variable length and constant cross-sectional area

 

 

prism

 

 

 

Sphere

 

 

sphere

 

 

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Pyramid - The equation is independent of the number of sides of the pyramid. So the equation works equally for a tetrahedron(with a triangular base) and for other solids with differently shaped base areas.

 

 

pyramid

 

 

 

Cone - This is similar to the pyramid, the area of the circle being the base area.

 

 

cone

 

 

 

Frustrum       This is the part of a cone remaining when a top section of the cone, parallel to the base, is removed.

 

volume of frustrum    =    [original vol. of cone]    -    [vol. of removed top section]

 

 

frustrum

 

 

 

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