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)

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

10-3 Surface Areas of Prisms and Cylinders

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

Surface Area of Circular Solids Lesson 12.3 cylinder cone sphere.

12 – 3 Cylinders and Cones.

Chapter 10. IMPORTANT! From Chapter 7, KNOW area formulas for: Triangles Rectangles Trapezoids Hexagons.

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.

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.

Warm-up Find the surface area of the prism below. 3 cm.

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.

The two shaded faces of the prisms shown are its bases An altitude of a prism is a segment joining the two base planes and perpendicular to both The faces.

Surface Area and Volume

12.3 Surface Area of Circular Solids

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

3/30 Take out paper and write the formula for a: Circumference Area Circle Area Parallelogram Area Triangle Area Regular Polygon Volume Rectangular Prism.

Geometry B Section 12.3 Surface Area of Pyramids and Cones.

PrismsPyramids Have 2 bases Named by the shape of the bases Have 1 base Lateral faces meet at one point Named by the shape of the base Pentagonal Prism.

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.

Geometry 12.2 – 12.5 Prep for the STAR Test. Geometry 12.2 Pyramids.

© 2010 Pearson Education, Inc. All rights reserved Concepts of Measurement Chapter 13.

Chapter 11: Surface Area & Volume

PRISMS. PARTS of a PRISM BASE FACE HEIGHT BASE FACE HEIGHT.

Surface Area and Volume of 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.

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, Lateral Area, and Volume of Prisms and Pyramids

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

Slide Surface Area  Surface Area of Right Prisms  Surface Area of a Cylinder  Surface Area of a Pyramid  Surface Area of a Cone  Surface Area.

Geometry Chapter 12 Review. Lateral Area of a Prism: L.A. Lateral Area of a Prism: L.A. The lateral area of a right prism equals the perimeter of a base.

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

Warm-Up 1) Draw a polygon that is not convex. 2) Find the measure of an exterior angle of a regular decagon. 3) Find the circumference and area of a circle.

Warm Up. Difference between a prism and a pyramid.

Chapter 12 Lateral and Surface Areas Lateral and Surface Areas of Prisms h L = Ph SA = L + 2B P = Perimeter of the base (bottom) h *base (shape.

 Def: A cylinder is a circular solid with two circular bases. r h L.A. = 2πrh S.A. = 2πrh +2πr 2.

8.2 Surface Area Objectives:

Chapter 10: Area & Volume 10.4, 10.5, 10.6 Space Figures Surface Area of Prisms, Cylinders, Pyramids, Cones, and Spheres.

Surface area & volume UNIT 4. Prisms SECTION 1  Prism: three dimensional shape with two parallel sides  Bases: sides parallel to each other  Lateral.

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.

Vertex Regular Pyramid – Slant Height - Altitude 1) Base is a regular polygon 2) Faces are congruent isosceles triangles 3) Altitude meets the base at.

 Cone: a solid with one base that is a circle, and a curved, smooth lateral surface that comes to a point, the apex. No, because it has a curved lateral.

Lesson : Prisms & Pyramids 1 Prisms and Pyramids.

Gaby Pavia and Gaby Pages. Section 12-1 Bases: congruent polygons lying in parallel planes Altitude: segment joining the two base planes and perpendicular.

Geometry Practice Test Prisms Find the (1) lateral area and (2) total area and (3) volume of the right prism (1) LA = pH LA.

Group 6 Period 5 Problems Mac Smith, Jacob Sweeny Jack McBride.

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.

CYLINDER, CONE AND SPHERE

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.

10-4 Surface Areas of Pyramids and Cones

Lesson 9-2: Prisms & Pyramids

Lesson 9-2: Prisms & Pyramids

Geometric Solids: Cylinders and Cones

Lesson 9-2 Prisms and Pyramids.

Lesson 9-3 Cylinders and Cones.

Lateral Area & Surface Area Of Pyramids & Cones

Lesson 9-2: Prisms & Pyramids

Lesson 9-2: Prisms & Pyramids

Lesson 9-2: Prisms & Pyramids

14 Chapter Area, Pythagorean Theorem, and Volume

Geometric Solids: Cylinders and Cones

Lesson 9-3: Cylinders and Cones

Lesson 9-3: Cylinders and Cones

Presentation transcript:

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) Volume: V = Bh Regular Pyramids: Lateral Area: L.A. = ½ lp (p = perimeter, l = slant height) Surface Area: S.A. = ½ lp + B (B = area of base) Volume: V = ⅓ Bh ( B = area of base, h = height)

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

Cylinders and Cones 3 Cones Surface Area (SA) = B + LA = π r (r + l) Cones are right pyramids with a circular base. Therefore, the formulas for pyramids can be used for cones. Volume (V) = Lateral Area (LA) = π r l, where l is the slant height. The base area is the area of the circle: Notice that the height (h) (altitude), the radius and the slant height create a right triangle. l r h Formulas: S.A. = π r ( r + l ) V =

Cylinders and Cones 4 Example: For the cone shown, find the lateral area surface area and volume. L.A.= πrl Note: We must use the Pythagorean theorem to find l. L.A.= π(6)(10) L.A.= 60π sq. cm. 6 cm = l 2 10 S.A.= πr (r + l ) S.A.= π6 (6 + 10) S.A.= 6π (16) S.A.= 96π sq. cm. V= 96π cubic cm.

Spheres 5 Surface Area & Volume of Sphere Volume (V) = Surface Area (SA) = 4 π r 2 Example:Find the surface area and volume of the sphere. 12 cm

Spheres 6 Surface Area & Volume of Hemisphere Find the surface area and volume of the following solid (Hemisphere). r= 12 cm