Illustration of a triangular prism; a prism whose bases are triangles.

Triangular Prism

Illustration of a triangular prism; a prism whose bases are triangles.

Diagram showing how "A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism and whose vertices are the three vertices of the upper base."

Truncated Triangular Prism

Diagram showing how "A truncated triangular prism is equivalent to the sum of three pyramids whose common…

An illustration of a prismatoid with 2 circular bases.

Prismatoid With 2 Circular Bases

An illustration of a prismatoid with 2 circular bases.

An illustration of a prismatoid with 2 circular bases.

Prismatoid With 2 Circular Bases

An illustration of a prismatoid with 2 circular bases.

An illustration of a prismatoid with circular base.

Prismatoid With Circular Base

An illustration of a prismatoid with circular base.

An illustration of a prismatoid with faces that are quadrilaterals.

Prismatoid With Quadrilateral Faces

An illustration of a prismatoid with faces that are quadrilaterals.

An illustration of a prismatoid with triangular faces and points labeled.

Prismatoid With Triangular Faces

An illustration of a prismatoid with triangular faces and points labeled.

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth the altitude into the sum of the two bases and four times the mid-section."

Volume of Prismatoid

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth…

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point, called the vertex." —Hallock 1905

Pryamid

"A pyramid is a solid whose base is a polygon, and whose sides are triangles uniting at a common point,…

Illustration used to compare the volumes of a pyramid and a prism by emptying sand from the pyramid into the prism.

Comparative Volumes Of A Pyramid And Prism

Illustration used to compare the volumes of a pyramid and a prism by emptying sand from the pyramid…

Illustration showing the cone being treated as a many-sided pyramid.

Relation Of Pyramid To Cone

Illustration showing the cone being treated as a many-sided pyramid.

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal pyramid. The stretched out image is created by drawing an arc with the perimeter of the base stepped off to create an intersection point.

Development Exercise of Oblique Hexagonal Pyramid

A sample exercise problem to complete the top part and create a stretched out image of the oblique hexagonal…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

The problem exercise in completing the top view and creating the development, or rolled out, image of the pentagonal pyramid.

Development Exercise of Pentagonal Pyramid

The problem exercise in completing the top view and creating the development, or rolled out, image of…

Illustration of the development of a pyramid. When the pyramid covered in paper (figure a) is rolled out on a flat surface, the result is shown in figure b.

Development Of Pyramid

Illustration of the development of a pyramid. When the pyramid covered in paper (figure a) is rolled…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum of a pyramid or a cone.

Pyramid Frustum

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has hexagonal bases, one with 10 inch side and the other with a 6 inch side. Height is 18 inches.

Pyramid Frustum With Hexagonal Bases and 6 inch and 10 inch Sides

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has right triangular bases, one with 20 inch side and the other with a 30 inch side. Height is 27 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has triangular bases with 14 inch sides. The other sides are 16 and 22 inches. The altitude is 24 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with a hexagonal base.

Pyramid With Hexagonal Base

An illustration of a pyramid with a hexagonal base.

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Inverted Pentagonal Pyramid

Illustration of an inverted pentagonal pyramid. It is pyramid with a regular pentagon for its base.

Illustration of the isometric of an oblique pentagonal pyramid.

Isometric of Oblique Pentagonal Pyramid

Illustration of the isometric of an oblique pentagonal pyramid.

Illustration of a plan and elevation of an oblique pentagonal pyramid.

Oblique Pentagonal Pyramid

Illustration of a plan and elevation of an oblique pentagonal pyramid.

An illustration of a regular pyramid with a square base and labels on lateral edge, slant height, altitude, and all corners.

Regular Pyramid With Square Base

An illustration of a regular pyramid with a square base and labels on lateral edge, slant height, altitude,…

Illustration of a spherical pyramid.

Spherical Pyramid

Illustration of a spherical pyramid.

Plan, front, and side views of a square pyramid.

Square Pyramid

Plan, front, and side views of a square pyramid.

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with vertical plane.

Square Pyramid Revolved 30°

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with vertical…

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with horizontal plane.

Square Pyramid Revolved 30°

Plan, front, and side views of a square pyramid after revolving pyramid through 30° with horizontal…

An illustration of a pyramid with a triangular base.

Pyramid With Triangular Base

An illustration of a pyramid with a triangular base.

An illustration of a rectangular prism with dimensions of 4 ft. by 1 ft. by 1 ft..

4 By 1 By 1 Rectangular Prism

An illustration of a rectangular prism with dimensions of 4 ft. by 1 ft. by 1 ft..

An illustration of a rectangular prism with dimensions of 4 ft. by 2 ft. by 1 ft..

4 By 2 By 1 Rectangular Prism

An illustration of a rectangular prism with dimensions of 4 ft. by 2 ft. by 1 ft..

An illustration of a rectangular prism with dimensions of 4 ft. by 2 ft. by 2 ft..

4 By 2 By 2 Rectangular Prism

An illustration of a rectangular prism with dimensions of 4 ft. by 2 ft. by 2 ft..

Illustration of the development of a rectangular prism. "Assume now that the prism is laid on the drawing board, the surface A face down, and the paper covering removed by turning the prism over and over, the paper remaining on the surface of the drawing board, as shown..."

Development Of Rectangular Prism

Illustration of the development of a rectangular prism. "Assume now that the prism is laid on the drawing…

The illustration of a rectangular pyramid unfolded by creating edges equal length to the base and meeting at point E.

Development of Rectangular Pyramid

The illustration of a rectangular pyramid unfolded by creating edges equal length to the base and meeting…

Illustration of a the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron with twelve equal pentagonal faces.

Bottom Half of a Regular Dodecahedron

Illustration of a the bottom half of a regular dodecahedron. A regular dodecahedron is a polyhedron…

Projection of a round bar.

Projection of Round Bar

Projection of a round bar.

Illustration of a spherical sector.

Spherical Sector

Illustration of a spherical sector.

Illustration of a spherical segments.

Spherical Segments

Illustration of a spherical segments.

Isometric of a prism with a semicircular top.

Prism With Semicircular Top

Isometric of a prism with a semicircular top.

Illustration of an oblique view of a rectangular solid/prism at 30°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 30°.

Illustration of an oblique view of a rectangular solid/prism at 45°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 45°.

Illustration of an oblique view of a rectangular solid/prism at 60°.

Oblique View Of Rectangular Solid

Illustration of an oblique view of a rectangular solid/prism at 60°.

An illustration of a rectangular solid/prism.

Rectangular Solid

An illustration of a rectangular solid/prism.

Illustration of model created by combining non regular geometric solids.

Combination of Geometric Solids

Illustration of model created by combining non regular geometric solids.

"A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant from a point within, called the center." —Hallock 1905

Sphere

"A sphere is a solid bounded by a uniformly curved surface, every point of which is equally distant…

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal diameters.

Development of Sphere Gore Method

An illustration in flattening the sphere using Gore method by creating cylinder sections with equal…

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

Development of Sphere Zone Method

An illustration of a development of sphere using Zone method by creating sections of rolled out cones.

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center. This illustration can be used to find the area of the zone and the volume of the segments.

Sphere With 8-inch Diameter Cut by Planes

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center.…

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

Sphere Cut Into Pyramids.

An illustration of a sphere cut into polygons as bases with their vertices at the center of sphere.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing how volume is found.

Sphere Inside of Cylinder.

An illustration of a sphere inside of a cylinder with radius/diameter labeled. Illustration for showing…

Illustration of a sphere inscribed in a cube.

Sphere Inscribed in a Cube

Illustration of a sphere inscribed in a cube.

Illustration of a sphere inscribed in a cube.

Sphere Inscribed in a Cube

Illustration of a sphere inscribed in a cube.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center.

Sphere with arcs and circles labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within, called the center. This shows the zones of a sphere.

Sphere With Arcs, Circles, and Zones Labeled.

An illustration of a sphere showing diameter, arcs, and circles. A sphere is a solid bounded by a curved…

Illustration showing that "the solids formed by the dissected part of the sphere are pyramids."

Sphere Formed By Pyramids

Illustration showing that "the solids formed by the dissected part of the sphere are pyramids."

An illustration of a sphere showing a radius of 1 foot. Illustration could be used for calculating volume.

Sphere With a Radius of 1 foot

An illustration of a sphere showing a radius of 1 foot. Illustration could be used for calculating volume.

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of one base.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are equal distances apart. This illustration is the segment of two bases.

Zones or Segments of Spheres

An illustration of a zone of a sphere. A zone occurs when a sphere is cut by parallel planes that are…

An illustration of a flanged spherical segment with a diameter of 10 inches. Illustration could be used to find the area.

Flanged Spherical Segment

An illustration of a flanged spherical segment with a diameter of 10 inches. Illustration could be used…