Chapter 9: Surface Area and Volume of 3-D Shapes



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Math II Project - Surface Area and Volume of 3-D Shapes

Group Assignment (maximum group size - 3 students) Due Monday May11, 2015

With your group, students must create a 3D object using the following shapes.

✓ Rectangular prisms

✓ Cube

✓ Cylinder

✓ Cone

✓ Sphere

✓ Right angle Pyramids

You are required to

✓ Calculate the surface area of each created object

✓ Calculate the volume of each created object

✓ Complete all assigned worksheet

✓ Submit all work in an organized well presented manner

You must use a minimum of 5 objects. This means that you must create the shape using nets. Your group may purchase an unlimited number 3D shapes for their project, but they are required to calculate the surface area and volume of the objects they have created.

If your group wishes to use a sphere you may purchase or use a pre-existing model (such as a tennis ball or Styrofoam ball). This object may be considered a “created item”.

The group must have at least 4 distinct shapes. You may not submit 4 different sizes of cubes!

Projects are due Thursday August 27, 2015. If the person in your group with the project is absent, the group will loose marks. It is your responsibility to submit it on time. Submit it early if you are unsure if you can make it to class on Thursday. The deadline for switching or dissolving your group is the end of class today.

Marks will be given to creativity of design and presentation of model.

Each Group member must turn in a completed worksheet with all work shown.

Please do not make your projects too big!

How your group can get an excellent mark

✓ Start the project ASAP. You can ask me questions all day every day.

✓ Share and compare your worksheet calculations with your group members or peers. Make sure you include all your units and steps

✓ Talk to other groups. You are not competing against each other! Share your ideas.

✓ Be original! Don’t use cardboard boxes. You can use chicken wire, pipe cleaners, straw, food, etc… If you would like to do the project using Flash, GSP or another program, talk to me.

✓ Submit your work early for constructive criticism.

✓ Discuss the group assessment with your group members. Assign the work accordingly. Poor group dynamics affect everyone’s mark!

✓ Write legibly! Include a title page, table of contents, and organize your answers and questions in a logical manner. Skip lines! Circle your answers! Reading your work should be easy!

Surface Area and Volume of 3-D Shapes Project Rubric

| |Level 1 |Level 2 |Level 3 |Level 4 |Marks |

|Knowledge | | | | | |

|(the |- Worksheets are incomplete |- Most of the worksheets are complete|- All 4 worksheets are complete |- All 4 worksheets are complete | |

|worksheets)|(approximately 50% complete) |(75%) |(90%) | | |

| | | | |- All steps are shown, and there are | |

| |- Calculations are incomplete |- Some steps are shown |- Most steps are shown, and there |only a few minor errors | |

| |or done with numerous errors | |are only a few minor errors | | |

| | |- There are some errors in the | |- Answers are clearly labelled | |

| |- Numerous steps are omitted |calculations | | | |

| | | | |- Word problems end with sentences | |

| |- Units are incorrect or | | | | |

| |missing | | | | |

| | | | | | |

| | | | | | |

|Application| | | | | |

|(The Model)|- Only 3 geometric shapes are |- Only 4 geometric shapes are |- 5 geometric shapes are created, |- 6 or more geometric shapes are | |

| |created |created, but models are not accurate |and most models are accurate |created, and the volume and SA are | |

| | |(cube isn’t a cube) | |calculated for each | |

| |- Model is created with little| |- Model is colourful and has a | | |

| |care for detail |- Some effort is apparent in model |theme |- Model is colourful, and has a theme| |

| | |design | |and well presented. | |

| |- Calculations for geometric | |- Calculations are correct | | |

| |shapes are incorrect, or |- Calculations for geometric shapes | |- Calculations are correct, and | |

| |contain many mistakes |contain errors |- Few steps are omitted |clearly labelled to corresponding | |

| | | | |objects | |

| |-Many steps are omitted |-Some steps are omitted | | | |

| | | | |- All steps are shown | |

|Communicati| | | | | |

|on |-Little effort is made to |- Some effort is made to organize |- Written work is neat and well |-Report is well presented, including | |

|(Presentati|organize material |material. |presented. |a title page, table of contents | |

|on and | | | |question sheet with answers following| |

|Organizatio|- Answers are not clearly |- Some answers are clearly identified|- 3D objects are well labelled and|it | |

|n) |identified | |identified | | |

| | |-Some 3D are not all clearly labelled| |-Answers are highlighted or circled. | |

| |-Few 3D shapes are labelled |(missing dimensions) |- Answers are clearly identified. |Word problems are answered with | |

| |and identified | | |sentences | |

| | |- Your project confuses me because it|- Your projects makes me happy | | |

| |- your project makes me angry |is disorganized. |because it is organized |- I proudly show your project to | |

| |because it is dysfunctional | | |other teachers because it is well | |

| |and illegible | | |written and organized. | |

|Peer / | | | | | |

|Teacher |- Group Assessment |- Group Assessment |- Group Assessment |- Group Assessment | |

|Assessment | | | | | |

| |- Your contribution was |- Your contributed less when compared|- Your contribution was equal to |- Your contribution was equal to your| |

| |minimal relative to your group|to your group members |your group members |group members, and you displayed a | |

| |members | | |leadership role in your areas. | |

| | |- You sometimes met with your group |- You regularly met with your | | |

| |- You did not meet regularly |members, but were not always |group members and were prepared to|- You always with your group members,| |

| |with your group members |prepared |work |with a ready action plan or agenda. | |

| | | | | | |

| |- You could not explain course|- You could explain some of the |- You could explain most of the |- You could explain all of the course| |

| |content to the teacher (you |course content to the teacher (you |course content to the teacher |content to the teacher (your test | |

| |cannot answer similar |answer some similar questions on a |(your test mark matches your |mark matches or exceeds your | |

| |questions on a test). |test) |knowledge/ application mark). |knowledge/ application mark). | |

Determining the Optimum Area and Perimeter

1. Make a chart of the possible dimensions for a rectangle with an area of 196 m2. What is the minimum perimeter for a rectangle with the given area?

2. Make a chart of the possible dimensions for a rectangle with a perimeter of 44 m. What is the maximum area for a rectangle with the given perimeter?

3. Determine the maximum area of a rectangle with a perimeter of

a) 232 km and b) 56 m

4. Determine the minimum perimeter for a rectangle with each area. Round your answer to the nearest 10th of a unit.

a) 242 cm2 and b) 1240 m2

Challenger (+5 e.c. points) Each of the following rectangles has a border on three sides. The area of each

rectangle is given. Determine the optimum length of their sides in order to minimize boarder

length.

a) 72 km2 and b) 162 m2

Problems Involving Composite Shapes

1. Calculate the shaded area of the figures below. Round your answer to the nearest 10th of a unit.

2. Calculate the area and the perimeter of each of the following shapes. Round your answers to one decimal place.

The Pythagorean Theorem

1. Determine the missing length. Round your answers to one decimal place

2. Determine the length of each missing side of the triangle. Round your answer to one decimal place.

Surface Area of Right Pyramids and Cones

1. Find the surface area of the following right pyramids. Round your answers to one decimal place

2. Find the surface area of the following cones

3. Find the surface area of a cone with a height of 4.0 km and a base area of 28.3 km2

Volumes of Pyramids and Cones

1. Calculate the volume of the following regular pyramids

2. Calculate the volume of the following cones

3. Find the height of a cone that has a radius of 2 cm and a volume of 23 cm3.

4. A cylinder has a volume of 2120.6cm3 and a base radius of 5 cm. What is the volume of a cone with the same height but a base radius of 2.5 cm?

Volume and Surface Area of a Sphere

1. Determine the surface are and volume of the following shapes

2. Find the surface area and volume of the following shapes

3. Eight basketballs are put into a holding container. The radius of each basketball is 10cm. How much room will be left in the container if the container is shaped like a square based pyramid with each side of the base measuring 40 cm and with a height of 70 cm?

Optimum Volume and Surface Area

1. Determine the least possible surface area of each object if it is a square based prism. Now determine the least possible surface area for each object if it is a sphere. Which area is smaller? Round your final answer to one decimal place.

a) 6859 m3 b) 6028.6cm3

2. Determine the least possible surface area for a cylinder with the following volumes. Round your answers to one decimal place.

a) 3217.0m3 b) 169.6mm3

Challenger (+10 points) Two shapes both have a surface are of 1200cm2. One of them is a cylinder and one of them is a square based prism.

a) What is the maximum value of the volume of the shape if it is a cylinder?

b) What is the maximum value of the volume of the shape if it is a square based prism?

c) Which shape should you chose for a container you are building if you want the greatest possible volume and the least possible surface are?

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Total Mark

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