S

Chapter 11 Surface Area and Volume

11.3 and 11.5

Essential Understanding

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

The volume of a pyramid is related to the volume of a prism with the same base and height

The volume of cone is related to the volume of a cylinder with the same base and height

Objectives

Students will be able to Find the surface area of a pyramid and a cone Find the volume of a pyramid and of a cone

Pyramids

Pyramid: polyhedron in which one face (the base) can be any polygon and the other faces (lateral faces) are triangles

Vertex: top of pyramid Slant height: length of the altitude of a lateral face of the

pyramid Assume a pyramid is a regular pyramid unless otherwise

stated

LA and SA of Pyramids

Lateral Area (LA): sum of the areas of the congruent lateral faces Half the product of the perimeter and the

slant height LA = ½ p l

Surface Area (SA): add the area of the base to the lateral area. SA = LA + B SA = ½ p l + B

When the slant height is not given you mustfind it first in order to find the LA or the SA

What is the Surface Area

What is the lateral area?

Volume of a Pyramid

V = 1/3 Bh

Cone

Base is a circle

Right Cone: altitude is a perpendicular segment form the vertex to the center of the base

Height is the altitude

Slant Height: distance from the vertex to a point on the edge of the base

LA and SA of a Cone

Lateral Area (LA): half the product of the circumference of the base and the slant height ½ * 2πr * l = π r l

Surface Area (SA): sum of the lateral area and the base LA + B π r l + πr2

What is the surface area in terms of pi?

Volume of a Cone

V = 1/3Bh

V = 1/3 π r2 h

Homework

Pg. 713

#10 – 22 even, 28 (8 problems)

Pg. 729

#6 – 18 even, 30 (8 problems)

16 problems total