Optimal Surface Area & Volume

Slides:

Advertisements

Similar presentations

3.7 Optimization Problems

Advertisements

Containers- Minimum area An Investigation Containers Consider the container It is required to design a box which satisfies the following requirements:-

SURFACE AREA and VOLUME of RECTANGULAR PRISMS and CUBES.

EXAMPLE 4 Solve a multi-step problem

Exercise If a pyramid and a cone have bases with the same area and altitudes that are equal, are their surface areas equal? no.

 Continue using a mat plan and its side and top views to represent a 3-D solid  Learn a new way to represent a 3-D object: net  Learn about a special.

Volumes Of Solids. 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 10cm.

CHAPTER 3 SECTION 3.7 OPTIMIZATION PROBLEMS. Applying Our Concepts We know about max and min … Now how can we use those principles?

Min-Max Problems Unit 3 Lesson 2b – Optimization Problems.

Maximizing Volume March 23, Profit and Product Distribution... Why does cereal come in a rectangular prism and potato chips come in a bag?

FILLING AND WRAPPING VocabularyPROBLEMSSURFACE AREA Miscellaneous VOLUME.

04/26/11 Changing Dimensions Today’s Plan: -Warm up -Changing Dimensions -Assignment LT: I will describe how increasing or decreasing a measurement will.

Chapter 12 Review.

Volume Performance Task Rectangular Prisms

4.4 Modeling and Optimization Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly,

1 The width, height, and length of a box or rectangular prism can be different. If all three are the same, then the box is a cube. Rectangular Prism The.

8.8: Optimum Volume and Surface Area

Volume of a Rectangular Prism

Holt CA Course Volume of Prisms and Cylinders MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures and.

What is Volume?. What is Volume? Volume is the amount of space inside an object.

LESSON 12.4 Volumes of Prisms and Cylinders. Volume The number of cubic units contained in its interior. (u 3 ) Volume of a Prism Demonstration.

Optimization. First Derivative Test Method for finding maximum and minimum points on a function has many practical applications called Optimization -

CHAPTER Continuity Optimization Problems. Steps in Solving Optimizing Problems : 1.Understand the problem. 2.Draw a diagram. 3.Introduce notation.

Make a Model A box company makes boxes to hold popcorn. Each box is made by cutting the square corners out of a rectangular sheet of cardboard. The rectangle.

12-2: Surface Areas of Prisms and Cylinders

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 12 cm 10cm.

VOLUME / SA FINAL REVIEW 1) Which statement best describes how the volume of a cube changes when the edge length is tripled (increased by a scale factor.

Geometry Volume of Cylinders. Volume  Volume – To calculate the volume of a prism, we first need to calculate the area of the BASE of the prism. This.

Chapter Volume of Pyramids and Cones Find the area of the base of the regular pyramid 1.Base is a regular hexagon Area of hexagon 2.

Volume of Prisms and Cylinders Algebra 2 1/18/2012.

We are learning to: - Enhance our Mathematical learning skills * solve volume problems Vocabulary: cross section cubic unit Always aim high! LESSON OBJECTIVES.

1 Volume: Lesson Objectives Understand the meaning of Volume Recognise the shapes of Prisms Determine the volume of Prisms.

VOLUME REVIEW. If r=7 units and x=7 units, then what is the volume of the cylinder shown below? r x.

VOLUME Volume – the amount of space, measured in cubic units, that an object or substance occupies. object.

Unit 8 Review: Measurement 7 th Grade. 1. Find the volume of the prism. a cubic cm b cubic cm c cubic cm d cubic cm.

Volume of Rectangular Prisms

Area, Perimeter, Surface Area, Volume

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 12 cm 10cm.

OPTIMIZATION PROBLEMS

Optimizing Area/SA/Volume

Containers- Minimum area

Welcome to Who Wants to be a Millionaire

Applied Max and Min Problems

Optimization questions

Volumes Of Solids. 7cm 5 cm 14cm 4cm 3cm 10cm.

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 10cm.

FILLING & WRAPPING 1.3 3) Warm-up:

4.6 Optimization The goal is to maximize or minimize a given quantity subject to a constraint. Must identify the quantity to be optimized – along with.

9.5 & 9.6 Optimization cylinders surface area & volume

Volume of solids.

Geometry Review PPT Finnegan 2013

Volume of a prism Example Find the volume of the cuboid below 4.7cm

What ordered pair represents the location of point C?

Volume of prisms and cylinders

Volume of Prisms and Cylinders

IMAGINE Find the area of the base, B, times the height

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

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 10cm.

Lesson 7: Optimizing Areas and Volumes of Rectangular Prisms

Finding the Volume of Any Prism or Cylinder and Any Pyramid or Cone

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 10cm.

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.

Unit 6 Measurement.

Volumes Of Solids. 8m 5m 7cm 5 cm 14cm 6cm 4cm 4cm 3cm 10cm.

Extending your knowledge Circumference of a circle =

Investigation 1 Building Smart Boxes Rectangular Prisms

Presentation transcript:

Optimal Surface Area & Volume Square-Based Prisms Cylinders

Note: Why do we want to minimize the surface area? To save money (costs less for packaging) To maximize the volume for a given surface area of a square-based prism, it is always a cube. To minimize the surface area for a given volume of a square-based prism, it is always a cube.

Example #1 Determine the dimensions of a square-based prism with a maximum volume, given the surface area of 864 m2. Calculate the volume.

Example #2 Tyler needs to construct a box to hold 6000cm3. What should the dimensions of the box be to minimize the amount of cardboard? Calculate the surface area of the box.

Note: The maximum volume for a given surface area of a cylinder will occur when the height and the diameter are equal. The minimum surface area for a given volume of a cylinder will occur when the height and the diameter are equal.

Example # 1 A fertilizer company wants to make a cylindrical storage container out of metal. There is 30m2 of material available. What are the dimensions of the container that would maximize the amount of fertilizer that can be stored? How much fertilizer could be stored?

Example #2 Baskin Robbins needs to design a cylindrical storage container that holds 1500cm3 of ice cream. What are the dimensions to minimize the amount of material needed? What is the amount of material needed?

Homework Pg. 480 # 1, 2, 5, 6, 11