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Honors Math 2 Name: __________________________ Cavalieri’s Principle (Section 9.12) Date: ___________________________ Cavalieri’s Principle: Two solids of the same height are cut by a plane so that the resulting cross sections have the same area. If the solids also have cross-­‐sectional areas equal to each other when cut by any plane parallel to the first, then they have the same volume. 1) Show that all pyramids that have the same height and the same base area must have the same volume. 2) A triangular pyramid and a square pyramid have equal volume and the same height, 3 inches. The base of the triangular pyramid has side lengths of 3 in, 4 in, and 5 in. Find the side length of the base of the square pyramid. Homework p. 775 #1-­‐4, 6-­‐8, 11-­‐13 Basic Vocabulary Prism: A solid with two congruent faces, called bases, that lie in parallel planes. The other faces, called lateral faces, are parallelograms formed by connecting the corresponding vertices of the bases. The altitude, or height, of a prism is the perpendicular distance between its bases. Right Prism: A prism whose lateral edges are perpendicular to both bases. Oblique Prism: A prism whose lateral edges are not perpendicular to the bases. The length of the oblique lateral edges is the slant height of the prism. Cylinder: A solid with congruent circular bases that lie in parallel planes. The altitude, or height, of a cylinder is the perpendicular distance between its bases. The radius of the base is also called the radius of the cylinder. Right Cylinder: A cylinder such that the segment joining the centers of the bases is perpendicular to the bases. Oblique Cylinder: A cylinder such that the segment joining the centers of the bases is not perpendicular to the bases. Pyramid: A solid in which the base is a polygon and the lateral faces are triangles with a common vertex. The altitude, or height, is the perpendicular distance between the base and the vertex. (Pyramids can be right or oblique) Cone: A solid with a circular base and one vertex. (Cones can be right or oblique) Sphere: The locus of points in space that are a given distance from a point, called the center of the sphere. Radius of a Sphere: A segment from the center of a sphere to a point on the sphere. Diameter of a Sphere: A chord that contains the center of the sphere. Great Circle of a Sphere: The intersection of a sphere and a plane that contains the center of the sphere. Hemisphere: Half of a sphere, formed when a great circle separates a sphere into two congruent halves. Cross-­‐Section: The intersection of a plane and a solid.