INTRODUCTION TO GEOMETRIC SOLIDS

OBJECTIVES Be able to recognize different types of geometric solids Be able to describe geometric solids using proper terminology Be able to draw nets of different types of geometric solids

GEOMETRIC SOLIDS Solid figures have THREE dimensions: Length Height Depth Plane figures have only two dimensions: length & height. Height Depth Length

GEOMETRIC SOLIDS The bottoms & tops of solids are called BASES The sides of solids are called LATERAL FACES or LATERAL AREAS Base Lateral Area Lateral Faces Base Base

SOLIDS WITH CURVED SURFACES! GEOMETRIC SOLIDS Two basic types of geometric solids: 1. Solids with flat surfaces called POLYHEDRONS 2. Solids with curved surfaces called SOLIDS WITH CURVED SURFACES!

A solid formed by polygons that enclose a single region of space is a POLYHEDRON

POLYHEDRONS The flat polygonal surfaces of the polyhedron are called A segment where two faces intersect is called an EDGE The point of intersection of three or more edges is called a VERTEX of the polygon

CONGRUENT, PARALLEL polygons. PRISMS A prism has two bases that are CONGRUENT, PARALLEL polygons. The lateral faces are rectangles or parallelograms that connect the corresponding sides of the bases. Prisms are classified by their bases.

PRISM

PYRAMIDS A pyramid has only one base. The lateral faces of a pyramid are triangles. The common vertex of the lateral faces is the vertex. Pyramids are classified by their bases.

PYRAMID

SOLIDS WITH CURVED SURFACES CYLINDERS A cylinder has two bases that are parallel and congruent. The bases of a cylinder are circles.

CYLINDER

CONES A cone has one base and a vertex. The base of a cone is a circle.

CONE

SPHERES A sphere is a set of all points in space at a given distance from a given point. The given distance is called the RADIUS of the sphere. The given point is at the CENTER of the sphere. Half of a sphere and its circular base is a hemisphere.

SPHERE

SURFACE AREA The SURFACE AREA of a geometric solid is the sum of the areas of all of the faces or surfaces that enclose the solid.

SURFACE AREA The surface area of a solid will be the sum of The area of its base(s) and The sum of the areas of its lateral faces, or, for a curved surface, the lateral area

To calculate the surface area of a solid, it is sometimes helpful to draw a NET

NETS A diagram of the faces of a geometric solid arranged in such a way that the diagram could be folded to form the solid What a geometric solid would look like if you cut it and smashed it out flat

PRISMS 5 cm. 5 cm. 5 cm.

PRISMS 10 in. 5 in. 20 in.

NET OF A PYRAMID

SLANT HEIGHT OF A PYRAMID Slant height is the altitude of the triangular face Slant height is the distance from the vertex of a regular pyramid to the midpoint of an edge of the base

NET OF A CYLINDER r H

NET OF A CONE

CONES = slant height of cone H = height of cone (Altitude) H r