Lesson Geometric Solids -- Prisms and Cylinders

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Lesson 59 -- Geometric Solids -- Prisms and Cylinders

Geometric Solids In Lesson 15 we defined a geometric solid as a geometric figure that has three dimensions. Below are some examples of geometric solids.

Prisms A prism is a geometric solid where two faces (called bases) are identical and parallel polygons and where the other faces are parallelograms (called lateral faces). The lateral faces intersect in segments called lateral edges of the prism. The altitude of a prism is a perpendicular segment joining the planes of the bases. The length of the altitude is the height of the prism. In the figures below a prism is show with component parts labeled.

Prisms Prisms are classified and named according to the shape of their bases. Below are four examples.

Cylinder A cylinder is like a prism except that its bases are circles instead of polygons. The curved surface between the bases is called the lateral surface. The segment joining the centers of the bases is called the axis of the cylinder. The altitude of a cylinder is a perpendicular segment joining the planes of the bases. The length of the altitude is the height of the cylinder. Below cylinders and their component parts are labeled.

Example 60.1 The area of a base of a right pentagonal prism is 28 cm2 and the length of a lateral edge is 10 cm. Find the volume of the right pentagonal prism.

Example 60.2 Find the lateral surface area of a right prism whose bases are regular pentagons. Dimensions are in meters.