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This publication presents formulas that can be used to find the radius of a ball (sphere) inscribed in a regular pyramid: triangular, quadrangular, hexagonal and tetrahedron.
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Formulas for calculating the radius of a ball (sphere)
The information below only applies to . The formula for finding the radius depends on the type of figure, consider the most common options.
Regular triangular pyramid
On the image:
- a – the edge of the base of the pyramid, i.e. they are equal segments AB, AC и BC;
- DE – the height of the pyramid (h).
If the values of these quantities are known, then find the radius (r) inscribed ball/sphere can be given by the formula:
A special case of a regular triangular pyramid is the correct one. For him, the formula for finding the radius is as follows:
Regular quadrangular pyramid
On the image:
- a – the edge of the base of the pyramid, i.e. AB, BC, CD и AD;
- EF – the height of the pyramid (h).
Radius (r) inscribed ball/sphere is calculated as follows:
Regular hexagonal pyramid
On the image:
- a – the edge of the base of the pyramid, i.e. AB, BC, CD, DE, EF, OF;
- GL – the height of the pyramid (h).
Radius (r) inscribed ball/sphere is calculated by the formula:
