Name Date Period. 3D Geometry Project
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- Evelyn Pearson
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1 Name 3D Geometry Project Part I: Exploring Three-Dimensional Shapes In the first part of this WebQuest, you will be exploring what three-dimensional (3D) objects are, how to classify them, and several formulas relating their three dimensions: length, width, and height. This is not meant to be a one-day project, so make sure you explore everything and answer the questions completely. First, go to: There are tabs along the top written in orange (Introduction, 3D Shapes, Surface Area & Volume, Euler s Theorem, Platonic Solids, and Test Your Skills). You will follow the Next arrow from each page to continue to the one. Anytime you come across a vocabulary word written in red, click on the word and you will be given its definition. Introduction 1. All objects can be measured in what three dimensions? 3D Shapes 1. What is a polyhedron? 2. Give three examples of polyhedra you see in everyday life. Prisms 1. What is a prism? 2. What is a net? 1
2 Name 3. What does it mean when a prism is described as a right prism? 4. Use the animation at the bottom of the page to complete the table below. Number of Faces Number of Vertices Number of Edges Triangular Prism Rectangular Prism Pentagonal Prism Octagonal Prism Pyramids 1. What is a pyramid? 2. What makes a pyramid different from a prism? 3. What does it mean when a pyramid is described as a right pyramid? 4. Use the animation at the bottom of the page to complete the table below. Triangular Pyramid Rectangular Pyramid Pentagonal Pyramid Hexagonal Pyramid Number of Faces Number of Vertices Number of Edges 2 Homework Assignment #1: Classifying Solids Worksheet
3 Name Surface Area & Volume 1. What is surface area? 2. What is volume? Surface Area Rectangles 1. How would you find the surface area of a rectangular prism? 2. Use the animation at the bottom of the page to find the surface area of the figure. What is the total surface area of the given rectangular prism? What is the formula for the surface area of a rectangular prism? Make sure to include what the variables represent (i.e., r = radius). S.A. rectangular prism = 3. Use the animation again to find the surface area of two more rectangular prisms. Length Width Height Surface Area Prism #1 Prism #2 Surface Area Cylinders 1. First use another resource to find the formulas for the area of a circle and circumference of a circle. Make sure to include what the variables represent (i.e., r = radius). Area circle = Circumference = 3
4 Name 2. What is the symbol we use for pi? What is the decimal approximation? 3. What is the formula for surface area of a cylinder? Make sure to include what the variables represent (i.e., r = radius). S.A. cylinder = 4. Use the animation at the bottom of the page to find the surface area of the figure. What is the total surface area of the given cylinder? Use the animation again to find the surface area of two more cylinders. Cylinder #1 Cylinder #2 Radius Height Total Surface Area Homework Assignment #2: Surface Area of Prisms and Cylinders Worksheet 5. Pyramids, cones and spheres are not included in this interactive. Use another resource to find the formulas for the surface area of pyramids, cones and spheres. Make sure to include what the variables represent (i.e., r = radius). Also, make sure to cite your resource. S.A. pyramid = S.A. cone = S.A. sphere = 4 Homework Assignment #3: Practice 10-6 Worksheet
5 Name Volume Rectangles 1. How many unit cubes does it take to fill the polyhedron? 2. What is the formula for finding the volume of a cube? Volume cube = 3. Use the animation again to find the volume of two rectangular prisms. Length Width Height Volume Prism #1 Prism #2 4. What is the formula for finding the volume of any rectangular prism? Volume rectangular prism = Volume Cylinders 1. Use the animation at the bottom of the page to find the volume of the given cylinder. 2. What is the formula for the volume of a cylinder? Volume cylinder = 3. Use the animation again to find the volume of two more cylinders. Radius Height Volume Cylinder #1 Cylinder #2 Homework Assignment #4: Practice 10-7 Worksheet 5
6 Name 4. Use another resource to find the formula for Volume of Pyramids & Cones. Make sure to include what the variables represent (i.e., r = radius). Also, make sure to cite your resource. Volume pyramid = Volume cone = Volume sphere = Homework Assignment #5: Practice 10-9 Worksheet Euler s Theorem 1. Use the animation at the bottom of the page to discover Euler s Theorem. Polyhedron Number of Faces Number of Vertices Number of Edges Triangular Pyramid Cube Pentagonal Prism Octagonal Prism Square Pyramid Hexagonal Pyramid Connected Pyramids 2. What is Euler s Theorem? 6 + =
7 Name Platonic Solids 1. What are the two things that make Platonic solids special? a. b. 2. Follow the directions to print all five Platonic solids. Color, cut and fold the net of each of the five Platonic solids. You will need colored pencils, scissors, and tape. Make sure to write your name on your solids before you fold them!!! 3. Use your folded Platonic solids and the animation at the bottom of the page to complete to following table. Polyhedron Faces Vertices Edges Type of Faces Tetrahedron Cube Octahedron Dodecahedron Icosahedron Number of Faces Meeting at Each Vertex Test Your Skills It is now time to assess how much you have learned about three-dimensional figures. Take some time now to look back and study the notes and answers you wrote down while you were exploring this website. You will be expected to know the surface area and volume formulas as well as Euler s Theorem. When you think you are ready to take the test, bring this packet up to the teacher, barrow a calculator, and select Test Your Skills. If you earned above 80%, please print the first results page and record your score below. You are now ready to proceed to Part II. You answered out of questions correctly. Your score is %. If you earned below 80%, click on See Your Results and look over the questions you answered incorrectly. Each question with an incorrect answer has a link for you to review what you did not understand. You may also get your packet back from your teacher to help you review. When you believe you have reviewed enough and are ready to re-take the text, ask your teacher for further instructions. 7
8 Name Part II: Cut & Fold Interactive: In Part II of this project you will be exploring the relationship between surface area and volume. We will be using the Three Dimensional Box Applet website to help us: Read through the instructions at the top of the page. Make sure to select the 8 by 10 size of graph. Use the animation to create 10 different sized boxes and complete the table below. Box #1 Box #2 Box #3 Box #4 Box #5 Box #6 Box #7 Box #8 Box #9 Box #10 Length (in) Width (in) Height (in) Volume (in 3 ) Surface Area (in 2 ) What did you notice about the relationship between the surface area and the volume? If you were going to make a popcorn box out of an 8x10 inch piece of paper, what dimensions would you use? Explain. 8
9 Name Part III: Popcorn Container: Imagine that you work for a packaging company, and your company is looking for a new package design to hold popcorn. Use the data you have collected over the past few days to design a container that will hold the most amount of popcorn kernels. You may only use one piece of 30 cm by 45 cm construction paper and tape/staples. The container can be any shape, as long as it is a shape you can calculate its surface area and volume. You will also be presenting your container to the class. Your presentation must include: The shape of your container and why you chose that particular shape A sketch of your shape labeled with its dimensions (i.e. length and width and height, or radius and height, etc ) The formula for its surface area & your calculations The formula for its volume & your calculations How many scoops of popcorn should fit inside (1 scoop = cm 3 ) Popcorn Container Rubric Accuracy of calculation of surface area /10 Accuracy of calculation of volume /10 Accuracy of number of scoops / 5 All group members participate in presentation / 5 Neatness & creativity of container / 5 Behavior & use of class time during project /10 Total /45 9
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