Working with models 4 Section Key term In this section you will work through an investigation in which you construct different 30 models and do various calculations involvall area and volume on those models. Application Act 10 models Application Activity: Investigation 2.2 The pictu of what th 2.2.1 W Squash balls and rectangular boxes sic Have you noticed that squash balls are often sold in rectangular WLOP DUNLOP 2.2.2 Re or boxes? This seems a bit strange given that squash balls are round i.e. spheres and so there must be lots of wasted space between the to round balls and the rectangular box. RACKETRALL DUNLOP RACKETBALL Throughout the remaining sub-sections below you are going to 2.2.3 investigate the following question: Would it not be more space - and cost - effective to package three squash balls in a cylindrical container rather than a rectangular box? Part 1: Determining the dimensions of a squash ball Width 2.3 The 1.1 Using the squash ball provided by your teacher, measure as (diameter) a W accurately as possible the width of the ball across its middle i.e. the diameter of the ball. Hint: A good way to do this is to position the ball between two books and to measure the length of the gap between the books. 1.2 Have a class discussion and reach agreement over the diameter of the ball so that everyone in the class is using the same value. 2.4 If your teacher does not have access to a squash ball, then: use a computer or cell phone to search the Internet for the standard diameter of a squash ball if you don't have access to the Internet, your teacher will be able to provide you with the dimension (it is provided in the Teacher's Guide). Part 2: Determining dimensions and building containers Length (Note: none of the pictures given below are drawn to scale). KETBALL 2.1 The picture alongside shows a 3D view of a rectangular box DUNLOP used for packaging 3 squash balls. RACKETBALL Use the diameter value that you determined in Part 1 above to write down the dimensions of the height, width and length of this box, and explain how you have determined these dimensions.h you will olving surface Application Activity: Investigation 2.2 The picture alongside shows a 2-dimensional net of what this box will look like when it is unfolded. 2.2.1 Write down the lengths / dimensions of the Glue flaps sides labelled A, B, C and D. 2.2.2 Redraw the net on a piece of thin cardboard or paper, if cardboard is not available. You must draw the net in real-size, i.e. according to the dimensions of what the rectangular box must be to fit three squash balls. Make the glue flaps 1 cm high. 2.2.3 Now fold the net along the dotted lines and glue the flaps to the sides adjacent to the flaps to form a 3-dimensional box. Dotted lines are fold lines Make sure that you don't glue the lid shut or you won't be able to get the squash balls inside. 2.3 The picture alongside shows a 3-dimensional view of a cylindrical container that could be used for packaging 3 squash balls. Note: the cylindrical box will need to have a lid and a bottom or base so that the balls don't fall out. Length What are the dimensions of the length, height and width of this cylindrical container? 2.4 The picture alongside shows a 2-dimensional net of what this cylindrical container will look like when it is unfolded. 2.4.1 Which side of the cylinder - the length, width B or height - does the side labelled 'A' represent? Glue flap Explain your answer and write down the dimension of side A. 2.4.2 Write down the dimension of the length indicated by the letter 'B'. 2.4.3 a. The dimension indicated by the letter 'C' is the same as the circumference of the lid or base. Explain why this is the case. fold line b. Use the formula below to determine the circumference of the lid and, hence, the dimension of the side labelled as 'C'. Round off the answer to one decimal place: Circumference = # X diameter ation Activity cor