Geometric Solids and Surface Area Geometry Regular Program SY 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 surface EDGE – segment where 2 polygons intersect VERTEX – point where 3 or more edges intersect

Classification of Polyhedra Polyhedra are classified according to the number of faces 6 faces7 faces10 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 Other faces are LATERAL faces, which are parallelograms LATERAL EDGES

PRISM - classified according to base

PRISM RIGHT vs OBLIQUE Lateral faces are rectangles.Lateral faces: NOT rectangles.

CYLINDER Has 2 parallel & congruent bases base LATERAL face

CYLINDER RIGHT vs OBLIQUE Axis is perpendicular to the circular base. Axis is NOT perpendicular to the circular base.

PYRAMID Has 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?

CONE Has only 1 base base LATERAL face Vertex of cone Slant height Height of cone

CONE RIGHT vs OBLIQUE

SPHERE

HEMISPHERE: Half a sphere PLUS the circular base The 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 slant height Total SA = 4 Congruent Triangular Faces + 1 square 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

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 Area Solve for the surface area of each given solid

Exercises on Surface Area Solve.

MORE Exercises on Surface Area Solve for the SA.

Exercises on Surface Area Solve.

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

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

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

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

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