Area and Volume of Solids Exam

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Surface Area of a Rectangular Prism

2lw + 2wh + 2lh

Cone

A cone is formed by a circular base and a curved surface that connects the base to a vertex.

Cylinder

A cylinder is formed by two parallel congruent bases (circles) and a curved surface that connects the bases.

Great Circle

A great circle is the largest circle that can be drawn on a sphere.

Prism

A prism is formed by two parallel congruent polygons called bases connected by faces that are parallelograms.

Pyramid

A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex.

Sphere

A sphere is the set of all points equidistant from a fixed point.

Lateral and Surface Area of a Right Rectangular Pyramid

LA = 1/2 (perimeter of base) (slant height) = 1/2 (P) (S) = (P/2) (S) SA = LA + Base Area

Lateral and Surface Area of a Prism

LA = base perimeter x height = ph SA = LA + 2 (base area)

Lateral and Surface Area of a Cylinder

LA = circumference x height = ch = 2πrh SA = LA + 2 (base area) = LA + 2πr²

Lateral and Surface Area of Right Circular Cones

LA = πrs SA = LA + Base Area

Surface Area

Surface area is the total area of all faces and curved surfaces of a three dimensional figure.

Surface Area of a Sphere

Surface area of a sphere is equal to the area of 4 great circles. SA = 4πr²

Height/Altitude of a Right Pyramid

The altitude or height of a pyramid is the perpendicular segment from the vertex to the plane of the base.

Lateral Edges

The edges that form the lateral faces of a solid.

Lateral Faces

The faces that join the bases of a solid.

Slant Height of a Right Pyramid

The slant height of a regular pyramid is the height of any of its lateral faces.

Lateral Area

The sum of the surface areas of all its faces excluding the base in a solid.

Volume of a Cone

The volume of a cone is 1/3 the volume of the cylinder with base area B and same height h. V = 1/3 (Base Area) (height) = 1/3 (πr²) (h)

Volume of a Cylinder

The volume of a cylinder is the product of the base area times the height of the cylinder. V = base area x height = πr²h

Volume of a Prism

The volume of a prism is the product of the base area times the height of the prism. V = base area x height = BA x h

Volume of a Pyramid

The volume of each pyramid is 1/3 the volume of the cube with a base area B and same height h. V = 1/3 (Base Area) (height) For a rectangular pyramid: V = 1/3 (lwh)

Volume of a Sphere

V = 4/3 πr³


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