ClipArt ETC
"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of the fluid. Immerse a solid cube one centimeter on each edge in water, so that its upper face shall be level and one centimeter below the surface of the liquid, as shown. The lateral pressures upon any two opposite vertical surfaces of the cube, as a and b, are clearly equal and opposite." -Avery 1895

Archimedies Principle

"It is evident that, when a solid is immersed in a fluid, it will displace exactly its own volume of…

Books on a shelf.

Books

Books on a shelf.

Sheet metal blank for making a cylindrical box with a diameter of 1 inch and a height of 2 inches.

Cylindrical Box - Blank

Sheet metal blank for making a cylindrical box with a diameter of 1 inch and a height of 2 inches.

A container used to measure a bushel.

Bushel

A container used to measure a bushel.

"To find the number of bushels of grain in a bin or box, multiply the length in feet by the height in feet, then by the width in feet and then by 8. For instance. In a bin 10 feet long, 6 feet high and 8 feet wide, 10 x 8 x 6 x 8 = 384." -Foster, 1921

Capacity

"To find the number of bushels of grain in a bin or box, multiply the length in feet by the height in…

An illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16 inches.

Vertical Cross Section of Spherical Zones of a Casting

An illustration of a vertical cross section of the spherical zones of a casting with a diameter of 16…

"Suppose our volume of hydrogen to unite with the volume of chlorine; if one particle of hydrogen combines with one particle of chlorine, it is evident that we should have four pairs; that is four particles of hydrogen chloride. These four particles of hydrogen chloride would occupy the same volume as four particles of hydrogen, or of chlorine, since dqual numbers of particles of gases occupy equal spaces. We should then expect one volume of hydrogen chloride to be formed." -Brownlee 1907

Combinational Volume

"Suppose our volume of hydrogen to unite with the volume of chlorine; if one particle of hydrogen combines…

"When one volume of hydrogen actually unites with one volume of chlorine, two volumes and not one volume of hydrogen chloride result. the volume of the acid is twice that of the hydrogen. Each of these two volumes must, according to Avagadro's hypothesis, contain four particles of the acid, or eight in all, so that in the eight particles of the acid there must be eight particles of hydrogen and eight particles of chlorine." -Brownlee 1907

Combinational Volume

"When one volume of hydrogen actually unites with one volume of chlorine, two volumes and not one volume…

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum edges range between 6 feet and 11 feet 5 inches and cylinder has a height of 12 feet.

Composite Figure of Quadrilateral Frustum With Half of a Cylinder Attached

An illustration of a composite figure made up of a quadrilateral frustum and half of a cylinder. Frustum…

Cross section of concrete conduit. The diagram can be used to find volume.

Cross Section of Concrete Conduit

Cross section of concrete conduit. The diagram can be used to find volume.

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into the cylinder.

Comparative Volumes Of A Cone And Cylinder

Illustration used to compare the volumes of a cone and a cylinder by emptying sand from the cone into…

An illustration of a circular cone.

Circular Cone

An illustration of a circular cone.

An illustration of a circular cone 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.

Circular Cone Frustum

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

"The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum."

Frustum of Cone to Find Volume

"The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose…

Illustration of a pyramid and with a regular polygon inscribed in and circumscribed about a cone. "If a pyramid whose base is a regular polygon is inscribed in or circumscribed about a circular cone, and if the number of sides of the base of the pyramid is indefinitely increased, the volume of the cone is the limit of the volume of the pyramid, and the lateral area of the cone is the limit of the lateral area of the pyramid."

Cone With Regular Polygon Inscribed and Circumscribed About

Illustration of a pyramid and with a regular polygon inscribed in and circumscribed about a cone. "If…

An illustration of a right circular cone with labels on slant height and altitude.

Right Circular Cone

An illustration of a right circular cone with labels on slant height and altitude.

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude (12).

Right Circular Cone

An illustration of a right circular cone with labels on slant height (12.422), radius (8), and altitude…

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Right Circular Cone 10 Feet High With 30 Degree Angle

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration could be used to find volume.

Right Circular Cone With 2 ft. Height and 1 ft. Radius

An illustration of a right circular cone with la radius of 1 foot and a height of 2 feet. Illustration…

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could be used for finding volume where subtraction is used.

Right Circular Cone With Hole Cut Out

An illustration of a right circular cone with labels on dimensions, and hole cut out. Illustration could…

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Comparative Volumes Of A Cone, Sphere, And Cylinder

Illustration used to compare the volumes of a cone, a sphere, and a cylinder.

Illustration of a cone with a polygon inscribed used to show that the volume of a circular cone is equal to one third the product of its base by its altitude.

Volume of Cone

Illustration of a cone with a polygon inscribed used to show that the volume of a circular cone is equal…

An illustration of a cube with the faces shaded.

Cube With Faces Shaded

An illustration of a cube with the faces shaded.

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

Cube for Illustrating Volume

An illustration of a cube divided into 6 equal pyramids to illustrate how volume can be found.

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by 8. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

128 Stacked Congruent Cubes

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by…

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

256 Stacked Congruent Cubes

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each.…

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by three cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by…

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a 3 by 3 by 3 cube. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

36 Stacked Congruent Cubes

Illustration of 36 congruent cubes stacked to resemble a 1 by 1 by 1 cube on a 2 by 2 by 2 cube on a…

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

64 Stacked Congruent Cubes

Illustration of 64 congruent cubes stacked so they form a cube that measures 4 by 4 by 4. A 3-dimensional…

Illustration comparing the fundamental units of measure 1 cubic yard and 1 cubic meter.

Comparison Of Units Of Cubic Measure

Illustration comparing the fundamental units of measure 1 cubic yard and 1 cubic meter.

Illustration of a right circular cylinder with a smaller cylinder removed from the center and placed next to it.

Cylinder Cut From a Cylinder

Illustration of a right circular cylinder with a smaller cylinder removed from the center and placed…

Illustration of a hollow cylinder.

Hollow Cylinder

Illustration of a hollow cylinder.

Illustration of a thin hollow cylinder. It resembles a washer and is often referred to as a disc.

Hollow Cylinder

Illustration of a thin hollow cylinder. It resembles a washer and is often referred to as a disc.

Illustration of a hollow cylinder viewed at an angle.

Hollow Cylinder

Illustration of a hollow cylinder viewed at an angle.

Illustration of a hollow cylinder viewed at an angle from above.

Hollow Cylinder

Illustration of a hollow cylinder viewed at an angle from above.

Illustration of a narrow right circular cylinder (with the height much smaller than the diameter) resting on its side/edge. This could also be described as a round disc.

Narrow Cylinder on Side

Illustration of a narrow right circular cylinder (with the height much smaller than the diameter) resting…

Illustration of a right circular cylinder.

Right Circular Cylinder

Illustration of a right circular cylinder.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

Right Circular Cylinder With 1 ft. Radius and 2 ft. height.

Right circular cylinder with a radius of 1 foot and a height/altitude of 2 feet.

Illustration used to show finding the volume of a pentagonal prism.

Volume Of Cylinder

Illustration used to show finding the volume of a pentagonal prism.

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters. Both cylinders (discs) are resting on a side/edge.

2 Narrow Cylinders on Their Sides

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters.…

Illustration of 2 similar cylinders. The height and diameter of the smaller cylinder is half that of the larger one.

2 Similar Cylinders

Illustration of 2 similar cylinders. The height and diameter of the smaller cylinder is half that of…

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

2 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 2 smaller congruent cylinders. The small cylinders are externally tangent…

Illustration of 2 soup cans that are similar cylinders. The diameter and height of the smaller can is one half that of the larger.

2 Soup Can Cylinders

Illustration of 2 soup cans that are similar cylinders. The diameter and height of the smaller can is…

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is 1/2 that of the previous one.

3 Similar Cylinders

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is…

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is one half that of the previous one.

3 Similar Cylinders

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is…

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

3 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 3 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

4 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 4 smaller congruent cylinders. The small cylinders are externally tangent…

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent to each other and internally tangent to the larger cylinder.

7 Smaller Cylinders In A Larger Cylinder

A large cylinder containing 7 smaller congruent cylinders. The small cylinders are externally tangent…

A decorative divider that resembles a book with bookmarks dangling on each side.

Book With Decorative Divider

A decorative divider that resembles a book with bookmarks dangling on each side.

Containers of dry measure in comparison: one bushel, peck, one half bushel, and one half peck. Illustration also shows liquid measures of quart and pint for comparison.

Dry Measures

Containers of dry measure in comparison: one bushel, peck, one half bushel, and one half peck. Illustration…

Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum of three pyramids (cones) whose common altitude is the altitude of the frustum and whose bases are respectively the upper base, the lower base, and a mean proportional between them."

Volume of Frustum of a Pyramid

Diagram used to prove the theorem: "The volume of the frustum of a pyramid (cone) is equal to the sum…

A Hempel Gas Burette is an instrument used to measure gases.

Hempel Gas Burette

A Hempel Gas Burette is an instrument used to measure gases.

"The Nicholson hydrometer of constant volume is a hollow cylinder carrying at its lower end a basket, d, heavy enough to keep the apparatus upright in water. At the top of the cylinder is a vertical rod carrying a pan, a, for holding weights, etc. The whole apparatus must be lighter than water, so that a certain weight (W) must be put into the pan to sink the apparatus to a fixed point marked on the rod (as c). The given body, which must weigh less than W, is placed in the pan, and enought weights (w) added to sink the point c, to the water line It is evident that the weight of the given body is W-w." -Avery 1895

Nicholson Hydrometer

"The Nicholson hydrometer of constant volume is a hollow cylinder carrying at its lower end a basket,…

Containers of liquid measure in comparison: one gallon, quart, pint, and gill.

Liquid Measures

Containers of liquid measure in comparison: one gallon, quart, pint, and gill.

Logarithmic graph (smooth curve) modeling the law of expansion with values of volume and pressure.

Logarithmic Graph of the Law of Expansion

Logarithmic graph (smooth curve) modeling the law of expansion with values of volume and pressure.

Illustration of a parallelopiped (a prism with a parallelogram as its base) used to demonstrate that the volume of any parallelopiped is equal to the product of its base by its altitude.

Parallelopiped Showing Volume

Illustration of a parallelopiped (a prism with a parallelogram as its base) used to demonstrate that…

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its base and its altitude."

Volume of Parallelopiped

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its…

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product of its three dimensions."

Volume of Rectangular Parallelopiped

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product…

A container used to measure a peck.

Peck

A container used to measure a peck.