JRLeon Geometry Chapter 8.6 HGSH

Any Way You Slice ItLesson 8.6

In Lesson 8.5, you discovered a formula for calculating the area of a circle. With the help of your visual thinking and problem-solving skills, you can calculate the areas of different sections of a circle.

JRLeon Geometry Chapter 8.6 HGSH

Any Way You Slice ItLesson 8.6

If you cut a slice of pizza, each slice would probably be a sector of a circle. If youcould make only one straight cut with your knife, your slice would be a segment of a circle. If you don’t like the crust, you’d cut out the center of the pizza; the crust shape that would remain is called an annulus.

A sector of a circle is the region between two radii and an arc of the circle.A segment of a circle is the region between a chord and an arc of the circle.An annulus is the region between two concentric circles.

JRLeon Geometry Chapter 8.6 HGSH

Any Way You Slice ItLesson 8.6

JRLeon Geometry Chapter 8.6 HGSH

Any Way You Slice ItLesson 8.6

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.6 Any Way You Slice It

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JRLeon Geometry Chapter 8.6 HGSH

Lesson 8.6 Any Way You Slice It

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.6 / 8.7 Any Way You Slice ItSurface Area

Class Work / Home Work: 8.6 Pages 455 – 457 : problems 1 thru 13, 178.7 Pages 466 : problems 1 thru 10

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaNot all building surfaces are rectangular. How would you calculate the amount of glass necessary to cover a pyramid-shaped building? Or the number of tiles needed to cover a cone-shaped roof ?

In this lesson you will learn how to find the surface areas of prisms, pyramids, cylinders, and cones. The surface area of each of these solids is the sum of the areas of all the faces or surfaces that enclose the solid. For prisms and pyramids, the faces include the solid’s bases and its lateral faces.In a prism, the bases are two congruent polygons and the lateral faces are rectangles or other parallelograms.In a pyramid, the base can be any polygon. The lateral faces are triangles

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaFind the surface area of the rectangular prism.

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaFind the surface area of the cylinder.

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaThe surface area of a pyramid is the area of the base plus the areas of the triangular faces. The height of each triangular lateral face is called the slant height. The slant height is labeled l and the pyramid height is labeled h.

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaSurface Area of a Regular Pyramid

You can cut and unfold the surface of a regular pyramid into these shapes.

bl = Area of the triangle and there are n triangles, where n = 8 sides.

bln = Area of the all the triangles.

ban = Area of the regular polygon.

bln + ban bn(l + a) P(l + a), where bn = perimeter P

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaSurface Area of a Cone

r2 = Area of the base of the cone

rl= Lateral Area of the cone.

r2 + rl = Surface Area of the cone

r(r + l) = Surface Area of the cone

JRLeon Geometry Chapter 8.6-8.7 HGSH

Lesson 8.7 Surface AreaFind the total surface area of the cone.

r(r + l) = Surface Area of the cone

5(5 + 10) = Surface Area of the cone

5(15) = Surface Area of the cone

(75) = Surface Area of the cone

75 = Surface Area of the cone

Surface Area of the cone is approximately 235.6 cm2