Surface Areas of Frustums

A frustum is that past of a pyramid or cone that lines between two parallel planes cutting it. If one of the planes is the base and the other is horizontal then the result is the shape shown below right (for a cone). The smaller cone top right and the original cone left are similar […]

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Ratios and Similar Shapes

If a shape is enlarged, so that all the sides are multiplied by the same factor, it will remain the same basic shape, the only difference being that all the sides are larger by the same factor. Sometimes though, we may deconstruct a diagram into similar shapes so that an enlargement exists from one shape […]

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Simultaneous Equations With One a Quadratic

When solving ordinary – linear – simultaneous equations we multiply the equations by constant factors to make the coefficient of some variable the same in magnitude, then add or subtract the equations to eliminate that variable. For example, solve  (1)  (2) (1)*2-(2)*3 eliminatesto give Substitution of this value ofinto (1) to find a gives If […]

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Constructing an Angle of 45 Degrees

To construct an angle of 45°, start by constructing a right angle. To construct a right angle use the circle theorem which says that a triangle inscribed in a circle, one edge of which is a diameter, is always a right angled triangle. Therefore, start by drawing a circle with a compass. The centre of […]

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