Geometric Solids and Surface Area Geometry Regular Program SY 2015-2016 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson

These DO NOT have CURVED surfaces. The Geometric Solids These DO NOT have CURVED surfaces. Observe that these have CURVED surfaces.

Observe that these also have CURVED surfaces. The Geometric Solids Observe that these also have CURVED surfaces.

FACE – each polygonal surface 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 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?

Has 2 parallel & congruent bases PRISM Other faces are LATERAL faces, which are parallelograms LATERAL EDGES base

- classified according to base PRISM - classified according to base

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

Has 2 parallel & congruent bases CYLINDER base LATERAL face base

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

Has only 1 base PYRAMID Vertex of pyramid LATERAL faces are triangles. LATERAL EDGES base

The slant height is the height of a triangular face. In a pyramid, there is a “slant height”. PYRAMID The slant height is the height of a triangular face.

- classified according to base PYRAMID Which of these pyramids are right? Oblique?

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

RIGHT vs OBLIQUE CONE

SPHERE

HEMISPHERE: Half a sphere PLUS the circular base The circle that encloses the base is the GREAT CIRCLE. If a plane cuts a sphere along the center, then the plane contains the great circle. If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-section? Is the equator In a globe a great circle?

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. Exercises Conservatories in Edmonton, Canada Containers in an ice cream plant in Burlington, Vermont

What solid is illustrated? Be specific. Exercises A bag of oranges

The surface area of any given solid is the 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.

STRATEGY! Draw each face. Get area of each face. Add all areas. SURFACE AREA Example A: STRATEGY! Draw each face. Get area of each face. Add all areas.

SURFACE AREA Solution:

SURFACE AREA Solution:

STRATEGY! Draw each face. Get area of each face. Add all areas. SURFACE AREA Example B: STRATEGY! Draw each face. Get area of each face. Add all areas.

SURFACE AREA Solution:

SURFACE AREA Solution:

How do we get the surface area of a pyramid? Example C: How do we get the surface area of a pyramid? STRATEGY! Draw each face. Get area of each face. Add all areas. Get area of TRIANGLES and the area of the BASE!

The pyramid has a square base with perimeter 48, and a height of 8 cm. SURFACE AREA Example C: The pyramid has a square base with perimeter 48, and a height of 8 cm. slant height 8 10 6 12 12 Total SA = 4 Congruent Triangular Faces + 1 square 12 12 10 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

How about the surface area of a cone? Example D: How about the surface area of a cone? Lateral face is a sector!

SURFACE AREA

PRISM CYLINDER PYRAMID CONE SURFACE AREA Total SA = Lateral Area + Base Area PRISM + CYLINDER PYRAMID CONE

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

Exercises on Surface Area Solve for the surface area of each given solid

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.

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 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 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)