Chapter on Formulas
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A collection of flashcards based on formulas related to polyhedra, prisms, pyramids, cylinders, cones, spheres, and frustums.
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24 Terms
Polyhedron
A solid whose faces are polygons.
Edge
The line where two faces of a polyhedron intersect.
Prism
A solid with two parallel and congruent bases connected by lateral edges.
Lateral edges
The edges that connect the corresponding vertices of the bases in a prism.
Lateral face
The faces of the prism that are not the bases.
Right prism
A prism whose lateral faces are rectangles.
Regular prism
A prism whose bases are regular polygons.
Lateral surface area
The sum of the areas of the lateral faces of a prism.
Total surface area
The sum of the lateral area and the area of the two bases in a prism.
Lateral area formula
LA = pH, where p is the perimeter of one base and H is the height of the prism.
Pyramid
A polyhedron with a polygon base and triangular lateral faces.
Regular pyramid
A pyramid with a regular polygon base and the apex directly above the base's center.
Surface area of a pyramid
SA = B + (1/2) * p * l, where B is the area of the base, p is the perimeter of the base, and l is the slant height.
Cylinder
A solid with two parallel circular bases.
Surface area of a cylinder
SA = 2πr² + 2πrh, where r is the radius and h is the height.
Lateral area of a cylinder
LA = 2πrh, where r is the radius and h is the height.
Cone
A solid with a circular base and a single vertex.
Lateral area of a cone
LA = πrl, where r is the radius and l is the slant height.
Surface area of a cone
SA = πr² + πrl, where r is the radius and l is the slant height.
Sphere
A perfectly round three-dimensional figure where every point on the surface is equidistant from the center.
Surface area of a sphere
SA = 4πr², where r is the radius.
Hemisphere
Half of a sphere, with surface area SA = 2πr².
Frustum
A cone with the top cut off, resulting in two circular bases.
Surface area of a frustum
SA = πR² + πr² + πl(R + r), where R is the radius of the larger base, r is the radius of the smaller base, and l is the slant height.
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