Surface area of pyramids and cones

Learning Objectives Define and identify the key components of pyramids and cones, including apex, base, altitude (height), and slant height. Apply the Pythagorean theorem to calculate the slant height or altitude of a right pyramid or cone when one is not given. Calculate the lateral area of regular pyramids and right cones using the appropriate formulas. Calculate the total surface area of regular pyramids by summing the lateral area and the area of the base. Calculate the total surface area of right cones by summing the lateral area and the area of the circular base. Solve multi-step, real-world problems involving the surface area of pyramids and cones. Ever wondered how much material is needed to make an ice cream cone or how ancient civilizations calculated the surface o...

TermDefinitionExample Regular PyramidA pyramid whose base is a regular polygon (all sides and angles are equal) and whose apex is directly above the center of the base. Its lateral faces are congruent isosceles triangles.The Great Pyramid of Giza is a regular pyramid with a square base. Right ConeA cone whose apex is positioned directly above the center of its circular base. The altitude is perpendicular to the base.A standard party hat or a traffic cone. Altitude (h)The perpendicular distance from the apex to the plane of the base. It is the 'true height' of the object, measured internally.In a cone, it's the line segment from the apex to the center of the circular base. Slant Height (l)The distance measured along the lateral surface from the apex to a point on the perimet...

Surface Area of a Regular Pyramid S.A. = B + L.A. = B + (1/2)Pl Use this formula to find the total surface area of a regular pyramid. 'B' is the area of the base polygon, 'P' is the perimeter of the base, and 'l' is the slant height. Surface Area of a Right Cone S.A. = B + L.A. = \pi r^2 + \pi rl Use this formula to find the total surface area of a right cone. 'r' is the radius of the circular base and 'l' is the slant height. Pythagorean Relationship l^2 = h^2 + r^2 For a right cone, the slant height (l), altitude (h), and radius (r) form a right triangle. Use this theorem to find any one of these lengths if the other two are known. A similar relationship exists in pyramids between the slant height, altitude, and apo...