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The equilateral cylinder is characterized by being a right circular cylinder in which the diameter of the base is equal to the value of the height (geratrix). [ 4 ] Then, assuming that the radius of the base of an equilateral cylinder is r {\displaystyle r\,} then the diameter of the base of this cylinder is 2 r {\displaystyle 2r\,} and its ...
For a given volume, the right circular cylinder with the smallest surface area has h = 2r. Equivalently, for a given surface area, the right circular cylinder with the largest volume has h = 2r, that is, the cylinder fits snugly in a cube of side length = altitude ( = diameter of base circle). [8]
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
A polyhedron with 2n kite faces around an axis, with half offsets tetragonal trapezohedron: Cone: Tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex: A right circular cone and an oblique circular cone Cylinder: Straight parallel sides and a circular or oval cross section
Within the cylinder is the cone whose apex is at the center of one base of the cylinder and whose base is the other base of the cylinder. By the Pythagorean theorem , the plane located y {\displaystyle y} units above the "equator" intersects the sphere in a circle of radius r 2 − y 2 {\textstyle {\sqrt {r^{2}-y^{2}}}} and area π ( r 2 − y ...
The volume of the cone is 1/3 its base area times the height. The base of the cone is a circle of radius 2, with area , while the height is 2, so the area is /. Subtracting the volume of the cone from the volume of the cylinder gives the volume of the sphere:
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The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex": =, where B 1 and B 2 are the base and top areas, and h 1 and h 2 are the perpendicular heights from the apex to the base and top planes. Considering that