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

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

Surface Area of Circular Solids Lesson 12.3 cylinder cone sphere.

12 – 3 Cylinders and Cones.

12-3. Pyramids  A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that.

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.

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

 A Polyhedron- (polyhedra or polyhedrons)  Is formed by 4 or more polygons (faces) that intersect only at the edges.  Encloses a region in space. 

12.3 Surface Area of Circular Solids

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)

11.3 Surface Areas of Pyramids and Cones A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces)

11 – 5 Volumes of Pyramids & Cones

Geometry B Section 12.3 Surface Area of Pyramids and Cones.

Chapter 11.3 Surface Areas of Pyramids and Cones.

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.

The Cone A Cone is a three dimensional solid with a circular base and a curved surface that gradually narrows to a vertex. Volume of a Cone = ++=

Surface Area of Pyramids and Cones SWBAT: Define Pyramid, Vertex of a pyramid, slant height, Regular Pyramid, Cone, and Right cone. Find the area.

Chapter 11: Surface Area & Volume

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.

Surface Area of Pyramids Pyramid – A polyhedron with all faces except one intersecting a vertex. Pyramids are named for their bases, which can be a polygon.

Surface Area, Lateral Area, and Volume of Prisms and Pyramids

Section 12.3 Surface Areas of Pyramids and Cones.

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.

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.

GEOMETRY 10.5 Surface Area of Pyramids and Cones.

Section 12.3 Notes.

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)

8.2 Surface Area Objectives:

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.

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.

11-3 Surface Areas of Pyramids and Cones

Lesson 72, day 2 Pyramids and Cones. Pyramids Pyramid: geometric solid with a polygon base, and triangle faces (lateral faces) Vertex: top of the pyramid.

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.

Surface Areas 8.7 Surface Area. Objective Apply the surface area formula to various 3-dimensional figures in order to find the area 8.7 Surface Area.

Boyd/Usilton.  A pyramid is a polyhedron in which one face (base) can be any polygon and the other faces (lateral) are triangles.  A regular pyramid.

Chapter 11: Surface Area and Volume Section 11-3: Surface Areas of Pyramids and Cones.

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

Surface Area of Pyramids Lesson Pyramids: Has only one base (polygon). Edges are not parallel but meet at a single point called the vertex. Lateral.

 A cylinder has two identical flat ends that are circular and one curved side.  Volume is the amount of space inside a shape, measured in cubic units.

CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-2 PYRAMIDS.

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.

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.

Chapter 12 Group 6 P Crowley C Prince C King K Connell.

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

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 and Volume of Pyramids Goal: Students will find the surface area and volume of pyramids.

Volume of Pyramids and Cones Section 9.5. Objectives: Find the volumes of pyramids and cones.

10-4 Surface Area of Pyramids and Cones

12.2 Surface Areas of Pyramids

12.3 – Surface Area of Pyramids and Cones

Section 12-2 Pyramids.

Lesson 9-2: Prisms & Pyramids

Lesson 9-2: Prisms & Pyramids

Geometric Solids: Cylinders and Cones

10-5 Surface Area of Pyramids & Cones

11.3 Surface Areas of Pyramids and Cones

12-2: Area and Volume of Pyramids

11.3 and 11.5: Pyramids and Cones

Surface Area and Volume of Pyramids

Lesson 9-2: Prisms & Pyramids

Surface Area of Pyramids

Lesson 9-3: Cylinders and Cones

Presentation transcript:

Vertex Regular Pyramid – Slant Height - Altitude 1) Base is a regular polygon 2) Faces are congruent isosceles triangles 3) Altitude meets the base at its center Not the same as lateral edge

Lateral Area – area of one face multiplied by number of sides Lateral Area can also be found by taking half the perimeter of the base times the slant height. L.A. = ½p l T.A. = L.A. + B V = Bh

Find the L.A., T.A. and Volume. 6in. 8in. 6in. 8in. 10 L.A. = ½p l L.A. = ½(12 · 4)(10) L.A. = 240 in² T.A. = L.A. + B T.A. = (12 · 12) T.A. = 384 in² V = Bh= (12 · 12)(8) V = 384 in³

Find the L.A.,T.A. and Volume. 6in. 5in. 3 5 L.A. = ½p l L.A. = ½(6 · 4)(5) L.A. = 60 in² T.A. = L.A. + B T.A. = 60 + (6 · 6) T.A. = 96 in² V = Bh= (6 · 6)(4) V = 48 in³ 4

Slant Height L.A. = ½·2πr ·l V = πr²h T.A. = πr l + πr² Altitude Cone – Just like a pyramid, but with a circular base

13m 24m Find the L.A., T.A. and Volume. 13m 12m 5 5 L.A. = ½·2πr ·l L.A. = π(12) · 13 L.A. = 156π T.A. = πr l + πr² T.A. = π(12 · 13) + π12² T.A. = 156π + 144π T.A. = 300π

13m 24m 5 V = πr²h V = π(12)²(5) V = 240π

Find the L.A., T.A. and Volume. 6 ft 3ft L.A. = ½·2πr ·l 3²+ 6²= x²x²= 45 L.A. = π(3) · L.A. = 9π T.A. = πr l + πr² T.A. = 9π + 9π T.A. = π(3 · ) + π3² V = πr²h V = π(3)²(6) V = 18π

A solid metal cylinder with radius 6cm and height 18cm is melted down and recast as a solid cone with radius 9cm. Find the height of the cone. V = πr²h V = π(6)²(18) V = 648π V = πr²h 648π = π(9)²h h = 24cm 648π = 27πh

A soup can has a height of 5 inches and a diameter of 6 inches. Determine the area of the label for the can. If 1 oz = 11.5 cubic inches, about how many ounces are in the soup can? L.A. = 2πrh L.A. = 2π(3)·5 L.A. = 30π V = πr²h V = π(3)²·5 V = 45π = in³ 12.3 oz.