9.5 & 9.6 Optimization cylinders surface area & volume

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9.5 & 9.6 Optimization cylinders surface area & volume

Agenda Take up Homework Questions Warm Up Lesson on Optimization of Cylinders Worksheets/Homework

Learning Goals Determine the minimum surface area for a given volume Solve problems involving maximizing the volume

Volume and Surface Area of a Cylinder

To maximize the volume The maximum volume for a given surface area of a cylinder occurs when its height equals its _________. That is, ___________ or _________ The dimensions of the cylinder with maximum volume for a given surface area can be found by solving the formula: and the height will be ________ that value, or _________

Substitute h = 2r into the formula for surface area of a cylinder to solve for the SA formula above:

Rearrange the formula to solve for height:

1. a. Find the dimensions of a cylinder with 1. a. Find the dimensions of a cylinder with maximum volume that can be made with 600cm2 of aluminum. Round the dimensions to the nearest hundredth of a centimetre.

1. b. What is the volume of this cylinder, to the 1. b. What is the volume of this cylinder, to the nearest cubic centimetre?

Minimize Surface Area of a Cylinder The minimum surface area for a given volume of a cylinder occurs when its height equals its ____________. That is, ___________ or ____________ The dimensions of the cylinder of minimum surface area for a given volume can be found by solving the formula: and the height will be ________ that value, or _________

Substitute h = 2r into the formula to solve for the V formula above:

2 a. Determine the least amount of aluminum 2 a. Determine the least amount of aluminum required to construct a cylindrical can with a 1 litre capacity, to the nearest square centimetre.

2 b. Describe any assumptions made.

Homework Pg. 508 # 1ac, 2, 3, 4, 8 Pg. 513 # 1ac, 2, 3, 4, 5, 6 UNIT Test Wednesday on Chapter 8 and Chapter 9 (all sections)

The hardest class Mr. Z has taught yet It was definitely an honour teaching you Grade 9’s. Every moment was a cherished memory whether it be from my favourite class saying “OooOo Clickers” or “Mr. Z, my god how many mistakes do you have on your worksheet” LOL. We’ve accomplished nearly 5 chapters in the 6 weeks I have been here, and all of you deserve a pat on the back. I wish you the best of luck in the future years to come, and I know for a fact that you will succeed throughout school