Area of a CircleThe formula for the area of a circle is:whereA = area of circler = radius of circle3.1416Since r = d/2 where d is the diameter of a circle, the formula for the area of acircle in terms of its diameter is:GEOMETRIC SOLIDSIn describing plane shapes, you use only two dimensions: width and length;there is no thickness. By adding the third dimension (thickness), you describe asolid object.Consider the solids described below.1. A PRISM is a figure whose two bases are polygons, alike in size and shape,lying in parallel planes and whose lateral edges connect corresponding vertices andare parallel and equal in length. A prism is a right prism if the lateral edge isperpendicular to the base. The altitude of a prism is the perpendicular distancebetween the bases.2. A CONE is a figure generated by a line moving in such a manner that oneend stays fixed at a point called the “vertex.” The line constantly touches a planecurve which is the base of the cone. A cone is a circular cone if its base is a circle.A circular cone is a right circular cone if the line generating it is constant in length.The altitude of a cone is the length of a perpendicular to the plane of the base drawnfrom the vertex.3. A PYRAMID is a figure whose base is a plane shape bounded by straightlines and whose sides are triangular plane shapes connecting the vertex and a lineof the base. A regular pyramid is one whose base is a regular polygon and whosevertex lies on a perpendicular to the base at its center. The altitude of a pyramid isthe length of a perpendicular to the plane of the base drawn from the vertex.4. A CIRCULAR CYLINDER is a figure whose bases are circles lying inparallel planes connected by a curved lateral surface. A right circular cylinder isone whose lateral surface is perpendicular to the base. (Note: Any reference in thistext to a cylinder will mean a circular cylinder.) The altitude of a circular cylinderis the perpendicular distance between the planes of the two bases.COMMON VOLUME FORMULASAll factors in the formulas must be in the same linear units. As an exampleone term could not be expressed in feet while other terms are in inches.AI-15

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