Chapter 12.1-12.3: Surface Area and Volume

Cylinder

A prism that has an infinite amount of lateral faces that have meshed together to become curved

Rectangular Prism

A prism that has rectangular bases. The bases are parallel and are connected by three similar rectangles

Triangular Prism

A prism that has triangular bases. The bases are parallel and are connected by three similar rectangles

Rectangular Pyramid

A pyramid that has a rectangle as its base, and all of the lateral faces are triangles. The lateral faces meet at an apex

Regular Pyramid

A pyramid that has a regular polygon for a base and lateral faces that are congruent isosceles triangles

Triangular Pyramid

A pyramid that has a triangle as its base, and all of the lateral face are also triangles. The lateral faces meet at an apex

Sphere

A solid shape that is perfectly round like a ball. A sphere has no faces, edges, or vertices

polyhedra

A solid with many flat faces

Hemisphere

Half of a sphere

Lateral Area of a Rectangular Pyramid

L.A.= (2)1/2bh (front and back) + (2)1/2bh (sides)

Lateral area of a Triangular Pyramid

L.A.= (2)1/2bh (front and back) + (2)1/2bh (sides)

Lateral Area of a Cone

L.A.= (pi)rl. Where r is the radius of the base and l is the slant height

Lateral Area of a Cylinder

L.A.= Ch or 2(pi)rh

Lateral Area of a Rectangular Prism

L.A.= Ph (P is the perimeter of the base and h is the height of the prism)

Lateral Area of a Triangular Prism

L.A.= bh(side 1) + bh(side 2) + bh(side3)

Total Surface Area of a Cone

T.S.A.= (pi)rl + (pi)r squared

Total Surface Area of a Cylinder

T.S.A.= 2(pi)rh + 2(pi)r squared

Total Surface Area of a Sphere

T.S.A.= 4(pi)r squared

Total Surface Area of a Triangular Pyramid

T.S.A.= L.A. + 1/2bh (area of the base)

Total surface Area of a Rectangular Prism

T.S.A.= L.A. + 2wh (area of the bases)

Total Surface Area of a Rectangular Pyramid

T.S.A.= L.A. + bh (area of the base)

Total Surface Area of a Triangular Prism

T.S.A.= bh(side 1) + bh(side 2) + bh(side3) + (2)1/2bh

Slant Height

The height of a lateral side in a three-dimensional figure

Lateral Edge

The line where the lateral faces meet to create an edge

Total Surface Area of a Hemisphere

2(pi)r squared

Cone

A 3-D shape with one circular base

Altitude

The vertical distance between the apex and the center of the base