S

Chapter 11 Surface Area and Volume

11.2 and 11.4

Essential Understanding

You can analyze a 3D figure by using the relationship among its vertices, edges, and faces

To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figure

You can find the volume of a prism or cylinder when you know its height and the area of its base

Objectives

Students will be able to recognize polyhedra and their parts Visualize cross sections of space figures Find the surface area of a prism and a cylinder Find the volume of a prism and the volume of a

cylinder

Polyhedron

A space figure, or 3D figure whose surfaces are polygons

Face: each polygon

Edge: segment formed by the intersection of two faces

Vertex: point where three or more edges intersect

Euler’s Formula

# Faces + # Vertices = # Edges + 2

Cross Section

The intersection of a solid and a plane.

A slice of the solid

What is the cross section formed?

Prisms

Prism: polyhedron with two congruent, parallel faces, called bases

Lateral faces: all the other faces

Prisms…

Right prism: the lateral faces are rectangles and a lateral edge is an altitude

Oblique Prism: some or all of the lateral faces are nonrectangular.

(For this chapter, assume that a prism is a right prism unless otherwise stated)

LA and SA of a Prism

Lateral Area (LA): sum of the areas of the lateral faces LA = ph

Surface Area (SA): sum of the lateral area and the area of the two bases SA = LA + 2B

What is the Surface Area?

What is the Surface Area? Lateral Area?

Volume of a Prism

Volume = Base times height

V = Bh

Cylinder

Two congruent, parallel bases that are circles

LA and SA of a Cylinder

Lateral Surface Area (LA): circumference of the base and the height of the cylinder LA = 2πr * h

OR LA = πdh

Surface Area (SA): Sum of the lateral surface area the two bases SA = LA + 2B SA = 2πrh + 2πr2

Volume of a Cylinder

Volume = Base times height

V = Bh

V = πr2h

Composite Space Figure

3D figure that is a combination of two or more simpler figures

To find the volume of a composite space figure, add the volumes of the figures that are combined

Homework

Pg. 704

#10 – 20 even, 26 (8 problems)

Pg. 721

#6 – 20 even, 38 (9 problems)

17 total problems