Surface Area of Pyramids and Cones

Slides:

Advertisements

Similar presentations

Chapter Area, Pythagorean Theorem, and Volume 14 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Advertisements

MFM1P Minds On Determine the volume of: a) This square based pyramid b) This triangular based pyramid.

Solids – Volume and Area We will be using primarily 4 solid objects in this lesson. Right Circular Cylinder Right Circular Cone r h r h s.

Here are a few terms Lateral edge Vertex Lateral face Altitude Base edge Base.

12.3 Surface Area of a Pyramids and Cones Slant Height ( l )

Surface Area of Pyramids & Cones Section Objectives Find the surface area of pyramids Find the surface area of cones.

Surface Area of Pyramids and Cones Section 12.3 Goal – to find the surface area of a pyramid and the surface area of a cone.

Standardized Test Practice

EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 = Write formula. l.

EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 = Write formula. l.

Geometry 11-3 Surface Areas of Pyramids and Cones.

Slant Heights of Pyramids and Cones LESSON 95. Slant Height The slant height is the distance from the base to the apex along the outside of the surface.

11.3 and 11.5: Pyramids and Cones. Pyramids Pyramid – A 3-D figure with one face (the base) that is any polygon and the other faces (the lateral faces)

10-4 Surface Areas of Pyramids

Geometry B Section 12.3 Surface Area of Pyramids and Cones.

10.6: Volumes of Pyramids and Cones Objective: To find the volume of pyramids and cones.

Section 12.3 Surface Area of Pyramids and Cones. Pyramid: polyhedron with one base lateral faces- triangles Slant Height: altitude of any lateral face.

10-4 Surface Areas of Pyramids and Cones

Section 12.3 Surface Areas of Pyramids and Cones.

MFM1P Minds On Determine the volume of the following shapes:

Warm Up. Difference between a prism and a pyramid.

 Lateral Surface Area : S = ½ P l  P represents the perimeter of the base and l represents the slant height  Total Surface Area : S = ½ P l + B 

Chapter Surface Area of Pyramids and Cones.

Surface Area of Pyramids and Cones Surface Area of a Pyramid.

Prisms & Pyramids 1 Prism and Pyramids Formulas Prisms: Lateral Area: L.A. = ph (p = perimeter, h = height) Surface Area: S.A. = ph + 2B (B = area of base)

Surface Areas of Pyramids Section Find the Surface Area… Find the surface area of a cylinder with a diameter of 10cm and a height of 15cm.

Surface Area of Pyramids and Cones Pyramid Cones Has a square base and comes to a point Has a circle base and comes to a point.

EXAMPLE 3 Standardized Test Practice SOLUTION To find the slant height l of the right cone, use the Pythagorean Theorem. l 2 = h 2 + r 2 l 2 =

Section 9.2 Nack/Jones1 Section 9.2 Pyramids, Area, & Volume.

Surface area & Volume of Pyramids Tutorial 13d Pyramids §A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces.

Lateral Surface Area Lateral Surface Area is the surface area of the solid’s lateral faces without the base(s).

Surface Area of a Cone and Pyramid. A cone has a circular base and a vertex that is not in the same plane as a base. In a right cone, the height meets.

Pyramid – a polyhedron with one base (a polygon) and triangular lateral faces that meet at a common vertex. Regular Pyramid – a pyramid with a regular.

12.3 Surface Area of Pyramids and Cones

MTH 232 Section 10.5 Surface Area.

Calculate Surface Area of Pyramids & Cones

10-4 Surface Areas of Pyramids and Cones

Warm Up Find the surface area of the right prisms.

9.3 Surface Area of Pyramids and Cones

9.2; 11-13, 24-26, ~ ~

12.3 – Surface Area of Pyramids and Cones

Surface Area of Pyramids

9-1B Surface Area of Pyramids

10-4 Surface Areas of Pyramids

Areas and Volumes of Similar Solids

Surface Areas of Prisms and Cylinders

Lesson 9-3 Cylinders and Cones.

Lesson 10.5 – 10.6 Surface Area of Prisms, Cylinders, Pyramids, Cones and Spheres Essential Question: How do you find the surface area of prisms, cylinders,

11.7A (11.4 – 11.7 Review) Prisms, Cylinders, Pyramids, Cones and Composite Solids: Surface Areas and Volumes Regular Polygons: A = ½ aP Central Angle/Triangle.

a)Sketch the region bounded by the lines y = 3, y = 1, x = 1, x = 6.

Objectives Learn and apply the formula for the surface area of a pyramid. Learn and apply the formula for the surface area of a cone.

11-3 Surface Area of Pyramids and Cones

10-4 Surface Areas of Pyramids

Surface Area of Pyramids and Cones

Lateral Area & Surface Area Of Pyramids & Cones

11.3 and 11.5: Pyramids and Cones

10-4 Surface Areas of Pyramids

Surface Area and Volume of Cones

Chapter 10 Extension Objective: To find missing dimensions

Given that they are equivalent, what is the diameter of the sphere?

Surface Area of Prisms and Cylinders

11.3 Surface Area of Pyramids and Cones

SOLIDS (3-D stuff) T BOLAN.

14 Chapter Area, Pythagorean Theorem, and Volume

11.3 Pyramids and Cones.

Surface Areas of Pyramids and Cones

12.3 Surface Area of Pyramids and cones

Section 8.2 Pyramids, Area, & Volume

Warm Up( Add to HW) Find the missing side length of each right triangle with legs a and b and hypotenuse c. 1. a = 7, b = c = 15, a = 9 c = 25 b.

Lesson 9-3: Cylinders and Cones

Presentation transcript:

Surface Area of Pyramids and Cones Section 12-3 Surface Area of Pyramids and Cones

Theorem 12-4 Surface Area of a Regular Pyramid The surface area S of a regular pyramid is where B is the area of the base, P is the perimeter of a base and l is the slant height.

If you are missing the slant height on a square pyramid, use the Pythagorean Theorem

Theorem 12-5 Surface Area of a Right Cone The surface area S of a right cone is where B is the area of the base, r is the radius of a base and l is the slant height.

If you are missing the slant height on a right cone, use the Pythagorean Theorem