Area and Volume of Solids Exam
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