Chapter 11-Volume

Oblique Cylinder

A cylinder that is not a right cylinder

tetrahedron

A polyhedron with four faces

Right prism

A prism whose lateral faces are rectangles. Its lateral edges are perpendicular to its bases.

Edge of a polyhedron

A segment where two faces intersect.

Polyhedron

A solid formed by polygons that enclose a single region of space. Just as a polygon is classified by its number of sides, a polyhedron is classified by its number of faces.

A prism

A special type of polyhedron, with two faces called bases, that are congruent, parallel polygons. The other faces of the polyhedron, called lateral faces, are parallelograms that connect the corresponding sides of the bases. Prisms are classified by their bases. For example, a prism with triangular bases is a triangular prism, and a prism with hexagonal bases is a hexagonal prism.

Regular polyhedron

If each face of a polyhedron is enclosed by a regular polygon, and each face is congruent to the other faces, and the faces meet at each vertex in exactly the same way. The regular polyhedron shown at right is called a regular dodecahedron because it has 12 faces.

Right Cylinder

If the axis of a cylinder is perpendicular to the bases

Right Cone

If the line segment connecting the vertex of a cone with the center of its base is perpendicular to the base

A cylinder

One solid with a curved surface. Like a prism, a cylinder has two bases that are both parallel and congruent. Instead of polygons, however, the bases of cylinders are circles and their interiors.

A cone

The base of it is a circle and its interior. The radius of a cone is the radius of the base. The vertex of a cone is the point that is the greatest perpendicular distance from the base. The altitude of a cone is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height of a cone.

faces of a polyhedron

The flat polygonal surfaces of a polyhedron. Although the face of a polyhedron includes the polygon and its interior region, we identify the face by naming the polygon that encloses it.

Lateral edge of a prism

The lateral faces meet to form those

The height of a prism

The length of an altitude

vertex of a polyhedron

The point of intersection of three or more edges of the polyhedron.

The axis of a cylinder

The segment connecting the centers of the bases.

cross-section

When a solid is cut by a plane, the resulting two-dimensional figure

Oblique prism

a prism that is not a right prism

A pyramid

is another special type of polyhedron. Pyramids have only one base. As in a prism, the other faces are called the lateral faces, and they meet to form the lateral edges. The common vertex of the lateral faces is the vertex of the pyramid. Like prisms, pyramids are also classified by their bases. The altitude of the pyramid is the perpendicular segment from its vertex to the plane of its base. The length of the altitude is the height of the pyramid.

Altitude of a prism

is any perpendicular segment from one base to the plane of the other base.

The altitude of a cylinder

is any perpendicular segment from the plane of one base to the plane of the other. The height of a cylinder is the length of an altitude.

A hemisphere

is half a sphere and its circular base. The circle that encloses the base of a hemisphere is called a great circle of the sphere. Every plane that passes through the center of a sphere determines a great circle. All the longitude lines on a globe of Earth are great circles. The equator is the only latitude line that is a great circle.

Volume

is the measure of the amount of space contained in a solid. You use cubic units to measure volume: cubic inches, cubic feet, cubic yards, cubic centimeters, cubic meters, and so on. The volume of an object is the number of unit cubes that completely fill the space within the object.

The radius of a cylinder

is the radius of a base.

A sphere

is the set of all points in space at a given distance from a given point. You can think of a sphere as a three-dimensional circle.The given distance is called the radius of the sphere, and the given point is the center of the sphere.