geom unit 4

Volume of a Prism/Cylinder

The volume of a prism/cylinder is V = BH, where B is the area

of the base and His the height of the solid. Remember that the formula you use to calculate the area of the base will depend on the shape.

The lateral surface of an object is all the sides of the object, excluding its base and top. The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.

The Lateral Surface Area formula is L = PH,

where P is the perimeter of the base and H is the height of the prism.

Surface Area of a Prism

SA = PH + 2B, where P is the perimeter of the base,

His the height of the prism, and B is the area of the base.

Term

Definition

altitude of a pyramid

a perpendicular line segment that joins the vertex to the plane of the base

base edge

one of the edges of a base of a prism or pyramid

height

the length of an altitude of a geometric figure

lateral edge

an edge of a polyhedron that is not a base edge

pyramid

a three dimensional figure with one base that is a polygon, and all other faces (called lateral faces) are triangles that meet at a single vertex

regular pyramid

a pyramid with a base that is a regular polygon and lateral faces that are congruent isosceles triangles

slant height

the length of the altitude of a lateral face of a pyramid

vertex of a pyramid

the common vertex at which the triangular faces meet

The volume of a pyramid is V = BH, where Bis

the area of the base and H is the height of the pyramid.

Term

Definition

slant height

the length of the altitude of a lateral face of a pyramid Think of a slant height as the distance up the side of a pyramid, cone, etc. It is not the height, which is fully at a right angle to the base.

Term

Definition

cone

a solid figure with a circular base and a curved surface that forms a point, or vertex, at the top

oblique cone

a cone whose axis is not an altitude

proportional

the characteristic of corresponding sets of values if every pair of values has the same ratio

Right Cone

Oblique Cone

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Volume of a Cone

The volume of a circular cone is V = 2 BH or

V = trIl, where B is the area of the base, His the

height of the cone, and r is the radius of the cone.

Surface Area of a Cone

The surface area of a right circular cone is

SA = nrl + tr, where r is the radius of the base

and l is the slant height.

The volume of a Sphere is V = 37r', where ris

the radius of the sphere.

Surface Area of a Sphere

The surface area of a Sphere is SA = 4r2, where

I is the radius of the sphere.