Solids

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A sudden paradigm shift…

A sudden paradigm shift…

Singular: polyhedronPlural: polyhedra A polyhedron is a three-dimensional solid figure in

which each side is a flat surface.The word polyhedron is derived from the Greek poly (meaning many) and the Indo-European hedron (meaning seat or face).

A polyhedron has no curved surfaces.

POLYHEDRONS

VS

POLYHEDRONS

POLYGONS

POLYGON POLYHEDRON

Has sides Has edges

2d 3d

plane space

or

POLYHEDRON

NOT

1. Toblerone Chocolate Box2. Magnolia Chocolait Container3. Doughnut 4. Ice Cream Cone5. A can of Milk6. Basketball7. Shoebox

These flat surfaces are polygons and are joined at their edges.

The polygons of a polyhedron are called faces, the common sides are called the edges and the points where these edges intersect are called the vertices.

POLYHEDRONS

A B C D

G H E F

POLYHEDRONS

A polyhedron is a prism iff two of its congruent faces are parallel and its other faces are parellelograms.

Prisms

base1

Lateral face

The two congruent faces of a prism are called the bases and the other faces are called the lateral faces.

Prisms

PrismsThe lateral faces are rectangles in a right prism, or parallelograms in an oblique prism. In a right prism, the joining edges and faces are perpendicular to the base faces.

PrismsParallelepipedA prism which has a parallelogram as its base is called a parallelepiped. It is a polyhedron with 6 faces which are all parallelograms.

PrismsThe edges of the prism where the lateral faces intersect are called its lateral edges. The lateral edges in a prism are congruent and parallel.

Lateral edges:There are 5 congruent and parallel lateral edges in this prism.

PrismsThe volume of a prism is the product of the base area times the height of the prism.

V = Bh(Volume of a prism:

B = base area, h = height)

PrismsThe surface area of a prism is the sum of the areas of the bases plus the areas of the lateral faces. This simply means the sum of the areas of all faces.

The surface area, S, of a right prism can be found using the formula S = 2B + ph.B = area of base, p = perimeter of base, h = height.

PrismsFind the volume and surface area of a cube that has an edge of 4cm.

PrismsFind the volume and surface area of a 3 ft right prism whose base is a rectangle with a length of 15ft and a width of 9ft.

PrismsThis figure represents a slab of cheese. It is in the form of a right triangular prism. Find the least amount of wrapping needed to cover the cheese on all sides.

SynthesisThe royal dance during the prom seemed memorable for AM and Kring that they became very close friends after the event. One day, AM bought a dozen of doughnuts for Kring. He noticed the box used for the doughnuts and remembered Mrs. Lumbre’s lesson.

The two bases are rectangle with a length of 20cm and width of 15cm. The box is 6cm tall. Solve for the volume and surface area of the box.

Synthesis

Assignment