Lesson 9-3 Cylinders and Cones.

Slides:

Advertisements

Similar presentations

1 Geometric Solids: Cylinders and Cones. Cylinders Cylinder: A right prism with circular bases. Therefore, the formulas for prisms can be used for cylinders.

Advertisements

Lesson 9-3: Cylinders and Cones

10-5 and 10-6 Volumes of Prisms, Cylinders, Pyramids, and Cones

Section 8.3 Nack/Jones1 8.3 Cylinders & Cones. Section 8.3 Nack/Jones2 Cylinders A cylinder has 2 bases that are congruent circles lying on parallel planes.

Volume of Cones and Pyramids

12 – 3 Cylinders and Cones.

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.

6.3: Surface Areas of Pyramids and Cones

Lesson 9-2: Prisms & Pyramids 1 Prisms and Pyramids Lesson 9-2.

Surface Area & Volume G.13.

LESSON THIRTY-SIX: DRAW LIKE AN EGYPTIAN. PYRAMIDS AND CONES So now that we have prisms under our collective belt, we can now begin to understand pyramids.

8 th Grade Math Chapter 9b Review. Chapter 9b Review 1)Give the formulas for: a)area of a circle b) circumference of a circle.

Prisms Lesson 11-2.

A sphere is the set of all points that are a given distance from a given point, the center. To calculate volume of a sphere, use the formula in the blue.

1 Prisms and Pyramids Mrs. Moy. Lesson 9-2: Prisms & Pyramids 2 Right Prisms Lateral Surface Area (LSA) of a Prism = Ph Total Surface Area (TSA) = Ph.

Chapter 10: Surface Area and Volume

Perimeter 1. Add all the sides 1 Area of a circle 2.

Lesson 12-5, 6, 13-2 Cones & Pyramids. Objectives Find lateral areas of regular pyramids Find surface areas of regular pyramids Find the volume of pyramids.

Chapter 11: Surface Area & Volume

The Pyramid Geometric Solids:. Solid Geometry Review: Solid Geometry is the geometry of 3D- dimensional space that we live in. The three dimensions are.

10-4 Surface Areas of Pyramids and Cones

Surface Area of Cylinders Unit 5, Lesson 3. What is a Cylinder? Definition: –A three dimensional figure with 2 circular bases. Formula for Surface Area:

Lesson 9-1: Area of 2-D Shapes 1 Part 1 Area of 2-D Shapes.

Grade 8 math chart TCU Is Going To The Rose Bowl!!!!!!!!!!!!!!!!!!!!

Warm Up. Difference between a prism and 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)

1 Cylinders and Cones. 2 Surface Area (SA) = ph + 2B = 2πrh + 2πr 2 Cylinders are right prisms with circular bases. Therefore, the formulas for prisms.

Lesson : Prisms & Pyramids 1 Prisms and Pyramids.

Surface Areas & Volume of Cylinders Tutorial 9a Lateral and Surface Area §A cylinder has two congruent parallel bases. §The bases of a cylinder are circles.

Chapter 12 Volume. Volume Number of cubic units contained in a 3-D figure –Answer must be in cubic units ex. in 3.

Chapter 10 Notes Area: Parallelograms Area of a figure is the number of square units it encloses. The stuff inside of a figure. Area of a Parallelogram:

Lesson 12-3 Cylinders and Cones (page 490) Essential Question How is the surface area and volume of pyramids and cones different from prisms and cylinders?

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

Surface area and Volume Ch Sol: G.10,12,13,14.

Cylinders and Cones Unit 12 Section 3 Identify the parts of cylinders and cones Find the lateral areas, total areas, and volumes of right cylinders and.

VOLUME OF A SOLID. VOLUME OF A PRISM OR CYLINDER V = Bh Where B is the area of the base and h is the height of the solid.

Prism & Pyramids. Lesson 9-2: Prisms & Pyramids2 Right Prism Lateral Area of a Right Prism (LA) = ph Surface Area (SA) = ph + 2B = [Lateral Area + 2 (area.

Surface area of a cylinder Imagine a cylinder opened out Rectangle Circle.

Calculate Surface Area of Pyramids & Cones

12.3 Surface Areas of Circular Solids

10-4 Surface Areas of Pyramids and Cones

Surface Area of Pyramids and Cones

REVIEW & PRACTICE for the Test

Lesson 9-2: Prisms & Pyramids

Surface Area and Volume Activity

Lesson 9-2: Prisms & Pyramids

Geometric Solids: Cylinders and Cones

Surface area and volume formulas

Volume of Prisms and Cylinders

Surface Area and Volume of Pyramids, Cones and Spheres

Lesson 9-2 Prisms and Pyramids.

11.2, 11.3 Surface Areas of Prisms, Cylinders, Pyramids, and Cones

11.6 Surface Area and Volume of Pyramids and Cones

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

Surface Areas of Prisms, Cylinders, Pyramids and Cones

NOTES 12.3 Surface Area of Circular Solids.

Surface Area of Pyramids and Cones

Lesson 9-2: Prisms & Pyramids

12.3 Surface Areas of Circular Solids

Surface Area and Volume of Cones

Chapter 10 Extension Objective: To find missing dimensions

Lesson 9-2: Prisms & Pyramids

Lesson 9-2: Prisms & Pyramids

Geometric Solids: Cylinders and Cones

Geometry Unit Formula Sheet

Lesson 9-3: Cylinders and Cones

9.4 – Perimeter, Area, and Circumference

Lesson 9-3: Cylinders and Cones

Presentation transcript:

Lesson 9-3 Cylinders and Cones

Cylinders Formulas: S.A. = 2πr ( r + h ) V = Cylinders are right prisms with circular bases. Therefore, the formulas for prisms can be used for cylinders. Surface Area (SA) = 2B + LA = 2πr ( r + h ) The base area is the area of the circle: The lateral area is the area of the rectangle: 2πrh Volume (V) = Bh = h 2πr h

Example For the cylinder shown, find the lateral area , surface area and volume. 3 cm S.A.= 2•πr2 + 2πr•h L.A.= 2πr•h 4 cm S.A.= 2•π(3)2 + 2π(3)•(4) L.A.= 2π(3)•(4) S.A.= 18π +24π L.A.= 24π sq. cm. S.A.= 42π sq. cm. V = πr2•h V = π(3)2•(4) V = 36π

Cones Formulas: S.A. = π r ( r + l ) V = l h r Cones are right pyramids with a circular base. Therefore, the formulas for pyramids can be used for cones. Lateral Area (LA) = π r l, where l is the slant height. Surface Area (SA) = B + LA = π r (r + l) l h The base area is the area of the circle: Volume (V) = r Notice that the height (h) (altitude), the radius and the slant height create a right triangle.

Example: For the cone shown, find the lateral area surface area and volume. S.A.= πr (r + l ) L.A.= πrl 6 cm 8 S.A.= π•6 (6 + 10) 62 +82 = l 2 10 S.A.= 6π (16) L.A.= π(6)(10) S.A.= 96π sq. cm. L.A.= 60π sq. cm. Note: We must use the Pythagorean theorem to find l. V= 96π cubic cm.

Thanks for coming!