Section 10 – 4 Surface Area Of Pyramids & Cones

Objective:To find the surface area of a Pyramid

To find the surface area of a Cone

Base:

A polyhedron with one base & all other faces are triangles that meet at a common vertex

Pyramid:

Any Polygon

Lateral Faces:Triangular Faces

VertexThe point at which all the lateral faces (triangles) meet.

Lateral Area:The area of the triangular faces.

Surface Area:

Example 1 Finding Surface Area of a

PyramidA) Find the lateral area and surface area of the hexagonal pyramid below.

B) Find the lateral area and surface area of a square pyramid with base edges 5 m and slant height 3 m.

C) Find the lateral area and surface area of a square pyramid with base edges 7.5 feet and slant height 12 feet.

Example 2 Finding Surface Area of a Pyramid

Part IIA) Find the lateral and surface area of the hexagonal pyramid below. Round to the nearest whole number.

B) The pyramid below models the Great Pyramid, built in Giza, Egypt. Find the lateral area of the Great Pyramid.

C) Find the lateral and surface area of the pyramid below.

HOMEWORK

Textbook Page 540; Find Lateral Area & Surface Area for #2, 3, 5, 6, 7, 10

𝐿 . 𝐴 .=96𝑚2

𝐿 . 𝐴 .=115 𝑖𝑛2

𝐿 . 𝐴 .=264 𝑖𝑛2S

𝐿 . 𝐴 .=24𝑚2 S

𝐿 . 𝐴 .=204𝑚2

S

Section 10 – 4

Continued…

Objective:To find the surface area of a cone

Base:Pointed like a pyramid, but has a circle base

Cone:

Circle

Slant Height :The distance from the vertex to a point on the edge of the circle.

Height :The distance from the vertex to the center of the circle.

Lateral Area:The area of the smooth surface.

Surface Area:

Example 3 Finding Surface Area of a

ConeA) Find the lateral and surface area of the cone in terms of π.

B) The radius of the base of a cone is 22 m. Its slant height is 10 m. Find the lateral and surface area in terms of π.

C) Find the lateral and surface area of the cone in terms of π.

Example 4 Real-World Connection

A) The funnel is in the shape of a cone. How much filter paper do you need to line the funnel?

B) Find the lateral area and surface area of a cone with radius 15 in. and height 20 in.

C) Leeann uses paper cones to cover her plants in the early spring. The diameter of each cone is 1 foot, and its height is 1.5 feet. How much paper is in the cone?

Ticket OutFind the lateral and surface area of each solid.

10 – 4 Ditto; #2 – 12 Even & hexagonal pyramids on back.