Geometric Solids and Surface Area

Geometry Regular ProgramSY 2014-2015

Sources:

Discovering Geometry (2008) by Michael Serra

Geometry (2007) by Ron Larson

The Geometric Solids

Observe that these have

CURVED surfaces.

These DO NOT have CURVED

surfaces.

The Geometric Solids

Observe that these also

have CURVED surfaces.

The Geometric Solids

A solid formed by polygons that enclose a single region of space is

called a POLYHEDRON (pl. polyhedra)

FACE – each polygonal surfaceEDGE – segment where 2 polygons

intersectVERTEX – point where 3 or more edges

intersect

Classification of Polyhedra

Polyhedra are classified according to the number of faces

6 faces 7 faces 10 faces

Classification of Polyhedra

How many faces does a tetrahedron have ?

REGULAR POLYHEDRON – a

polygon whose faces are congruent regular

polygons

Which are polyhedra?

PRISM Has 2 parallel & congruent bases

base

base

Other faces are LATERAL faces,

which are parallelograms

LATERAL EDGES

PRISM

- classified according to base

PRISMRIGHT vs OBLIQUE

Lateral faces are rectangles.

Lateral faces: NOT rectangles.

CYLINDER Has 2 parallel & congruent bases

base

base

LATERAL face

CYLINDERRIGHT vs OBLIQUE

Axis is perpendicular to the circular base.

Axis is NOT perpendicularto the circular base.

PYRAMIDHas only 1 base

base

LATERAL faces are triangles.

LATERAL EDGES

Vertex of pyramid

PYRAMID In a pyramid, there is a “slant height”.

The slant height is the height of a triangular

face.

PYRAMID- classified according to base

Which of these pyramids are

right? Oblique?

CONEHas only 1 base

base LATERAL face

Vertex of cone

Slant height

Height of cone

CONERIGHT vs OBLIQUE

SPHERE

HEMISPHERE: Half a sphere PLUS the circular baseThe circle that

encloses the base is the GREAT

CIRCLE.

If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-

section?

If a plane cuts a sphere along the center, then the

plane contains the great circle.

Is the equator In a globe a great circle?

Exercises What solid is illustrated? Be specific.

Exercises What solid is illustrated? Be specific.

Exercises What solid is illustrated? Be specific.

Exercises What solid is illustrated? Be specific.

Conservatories in Edmonton, Canada Containers in an ice

cream plant in Burlington, Vermont

Exercises What solid is illustrated? Be specific.

A bag of oranges

What is SURFACE AREA?The surface area of any

given solid is the SUM of the areas of ALL EXPOSED and TANGIBLE faces that enclose the

solid.

SURFACE AREA

Example A:

STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.

SURFACE AREA

Solution:

SURFACE AREA

Solution:

SURFACE AREA

Example B:

STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.

SURFACE AREA

Solution:

SURFACE AREA

Solution:

SURFACE AREA

Example C:

How do we get the surface area of a pyramid?

STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.

Get area of TRIANGLES and the area of the BASE!

SURFACE AREA

Example C: The pyramid has a square base with perimeter 48, and a height of 8 cm.

8

1212

6

slant height

10

10

12

Total SA = 4 Congruent Triangular Faces + 1 square

12

12

SURFACE AREA

Example D:

Is there a formula to get the surface area of a right pyramid with a regular base?

Solution:

Lateral Area + Base Area

SURFACE AREA

SURFACE AREA

Example D:

How about the surface area of a cone?

Lateral face is a sector!

SURFACE AREA

Total SA = Lateral Area +

Base Area

PRISM +

CYLINDER

+

PYRAMID

+

CONE +

SURFACE AREA

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve for the surface area of each given solid

Exercises on Surface AreaSolve.

MORE Exercises on Surface AreaSolve for the SA.

Exercises on Surface AreaSolve.

Exercises on Surface AreaSolve.

MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)

MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)

MORE Exercises on Surface AreaExpress the SA of each solid (no answers given)

MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)

MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)

MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)

MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)