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