Platonic solid the inradius "r". That is, The following table lists the various radii of the Platonic solids together with their surface area and volume. The overall size is fixed by taking the edge length, "a", to be equal to 2. The constants "φ" and "ξ" in the above are given by Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere. The icosahedron has the largest number of faces and the largest dihedral angle, it hugs its inscribed sphere the most tightly, and its surface area to volume ratio is closest
Solid of revolution suitable integral. The disk method is used when the slice that was drawn is "perpendicular to" the axis of revolution; i.e. when integrating "parallel to" the axis of revolution. The volume of the solid formed by rotating the area between the curves of and and the lines and about the -axis is given by If (e.g. revolving an area between the curve and the -axis), this reduces to: The method can be visualized by considering a thin horizontal rectangle at between on top and on the bottom, and revolving it about the -axis; it forms a ring (or disc in