R R² R³. When two figures are similar, the following is true. The ratio of their sides is the same as the ratio of their perimeters. RATIO: 3:4 3 6 4.

Slides:

Advertisements

Similar presentations

1.3 Surface Areas of Objects Made from Right Rectangular Prisms

Advertisements

Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

A demonstration on how to find the volume of rectangular prisms.

Finding Surface Area Step 1: Flatten the 3-D figure A rectangular prism will flatten to 6 rectangles. Depending on the dimensions of the 3-D figure, you.

Chapter 10 Review Game. Lessons 10-6 Solid Figures 1, 2, 3, 4, 5, Surface Area 1, 2, 3, 4, 5, Finding Volume 1, 2, 3, 4, 5,

Changes in scale. Find the volume of the cube 5m V = BhB = area of the base B = 5 5 B = m³ 25 B = ,000 m³ 2500 V = BhB = area of the.

SURFACE AREA and VOLUME of RECTANGULAR PRISMS and CUBES.

Today we will investigate the volume of cubes. DESCRIPTION OF A CUBE  WHAT IS A CUBE?

LESSON How do you find the volume of a rectangular prism. Volume of Rectangular Prisms 10.1.

11-7 Areas and Volumes of Similar Solids. Problem 1: Identifying Similar Solids Are the two rectangular prisms similar? If so what is the scale factor.

Surface Area and Volume Three-Dimensional Figures and.

Solid Figures: Volume and Surface Area Let’s review some basic solid figures…

Volume of Rectangular Prisms

A cube has a total surface area of 24 cm2

Measurement Jeopardy CirclesPerimeter Area 3-D Surface Area And Volume $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.

The area of a rectangle equals its length times the width (base times the height). A = length x width = lw or A = base x height = bh Area of a Rectangle.

Prisms Lesson 11-2.

Surface Area of Prisms Unit 5, Lesson 2. What is a Prism? Definition: –A three dimensional figure with 2 congruent polygon bases and rectangular sides.

12.7 Similar Solids. Definitions of Similar Solids Similar Solids have congruent angles and linear measure in the same ratios. Scale factor 9 : 3 Perimeter.

Surface Area & Volume of Prisms Tutorial 5c Lateral and Surface Areas of Prisms §The lateral area of a prism is the sum of the areas of the lateral faces.

Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

Volume word problems Part 2.

3D Figures What is a 3D figure? A solid shape with length, width, and height rectangular prisms cube cone cylinder pyramid.

VOLUME Volume is a measure of the space within a solid figure, like ball, a cube, cylinder or pyramid. Its units are at all times cubic. The formula of.

Pyramids Surface Area and Volume. Suppose we created a rectangular pyramid from a rectangular prism. Suppose we conducted an experience similar to yesterday’s.

Course Changing Dimensions Warm Up Find the surface area of each figure to the nearest tenth. Use 3.14 for . 1. a cylinder with radius 5 ft and.

Changing Dimensions: Surface Area and Volume. Recall that similar figures have proportional side lengths. The surface areas of similar three-dimensional.

10-8 Areas and Volumes of Similar Solids

Warm Up A shape has 5 faces, and 5 vertices how many edges does the shape have? A sphere has a radius of 7.5, what is its surface area and volume? What.

6-1 Lesson 6-1 Example 1 Find the number of faces, vertices, and edges. Identify the figure. 1.How many faces? Example

Week 24 - Vocabulary 3-Dimensional Figures.

Volume The perimeter of a shape is the total distance around the edge of a shape. Perimeter is measured in cm The Area of a plane figure is the amount.

Three-Dimensional Figures – Identify and use three-dimensional figures.

Unit 8, Lesson 4 Surface Area Standard: MG 3.0 Objective: Find the volume and surface area of prisms and cylinders.

Surface Area and Volume of Similar Figures Section 12.7.

Course 2 Unit 5 Lesson 7 Unit 5 Lesson 7 Properties of Volume and Surface Area Properties of Volume and Surface Area.

VOLUME OF SOLID FIGURES BY: How To Find The Volume First find the area ( A ). A =  r square Then multiply the area ( A ) times the height ( H ). V =

Chapter 9 Geometry © 2008 Pearson Addison-Wesley. All rights reserved.

Unit 5 Lesson 8 Unit Review. If a number is a perfect cube, then you can find its exact cube root. A perfect cube is a number that can be written as the.

Changes in scale.

Practice Quiz Polygons, Area Perimeter, Volume.

Percent Change of Dimensions Lesson 71. Increase and Decrease ›Increase: Dilation ›Decrease: Reduction ›Creates similar figures; proportional measures.

Exploring Solids and Shapes. Basic Definitions Face: A flat surface on a solid figure. Edge: A line segment where two faces meet Vertex: A point where.

Bell Work: What is the volume of the box with the dimensions shown? 4 inches 5 inches 9 inches.

Similarity. Do Now What is the volume of the prism below: 3 in 2 in 7 in.

Scaling Three-Dimensional Figures

Section 11-7 Ratios of Areas.

Mathematics Volume.

10-2 & 10-3: Representations of 3-D Figures and Surface Area of Prisms

Surface Area of a Prism.

Topic 10: Understand Volume Concepts Vocabulary

Objective - To find the surface area of a rectangular prism.

Three Dimensional Figures

Three –Dimensional Figures

How dimension change affects surface area and volume.

Square and Cube Roots.

11.7: Surface Area and Volume for Similar Solids

U8D7 Have out: Bellwork: r=

Drill Solve for x: Find the surface Area of a rectangular prism if the dimensions are 3 x 5 x 6. Find the volume of a right cylinder with radius 5 cm.

Volume Ratios of Similar Solids

Volume ratios of similar solids

Cross Section Craziness

Geometry Unit Formula Sheet

I have 4 faces. I have 6 edges. I have 4 vertices.

Geometry/Trig 2 Name: ____________________________________

Volume of Prisms, Cross Sections and Scale Factors

Presentation transcript:

R R² R³

When two figures are similar, the following is true. The ratio of their sides is the same as the ratio of their perimeters. RATIO: 3: Perimeter ₁: = 18 Perimeter₂: = 24 18:24 REDUCES TO 3:4

When two figures are similar, the following is true. The ratio of their area is the ratio of their sides “squared”. RATIO: 3:4 RATIO²: 9: Area₁: (3 x 6) = 18 Area₂: (4 x 8) = 32 Ratio²: 18:32 REDUCES TO 9:16

When two figures are similar, the following is true. The ratio of their volume is the ratio of their sides “cubed”. RATIO: 3:4 RATIO³: 27: Volume₁: (3 x 6 x 6) = 108 Volume₂: (4 x 8 x 8) = 256 Ratio³: 108:256 REDUCES TO 27:64

Suppose the ratio of the sides of 2 cubes is 3:5. Then the ratios of their surface are is …. What is the ratio of their volume? RATIO of sides is 3:5 RATIO of surface area (3:5) ² = (9:25) RATIO of volume (3:5)³ = (27:125)

The tetrahedra have a ratio of 3:5. If the volume of the small tetrahedron is 65 cubic units, then the volume of the large tetrahedron is... We are dealing with volume so we will use r³ (3/5)³ = 27/125 soooooo 65/Vlg = 27/125 cross multiply 125(65) = 27(Vlg) Divide cubic units

Two rectangular prisms are similar. Suppose the ratio of their vertical edges is 3:8. Use the r:r²:r³ Theorem to find the following without knowing the dimensions of the prism. a) Find the ratio of their surface areas. b) Find the ratio of their volumes. c) The perimeter of the front face of the large prism is 18 units. Find the perimeter of the front face of the small prism. d) The area of the front face of the large prism is 15 square units. Find the are of the front face of the small prism. e) The volume of the small prism is 21 cubic units. Find the volume of the large prism.