HOPE Charter School 2009 PSSA Boot Camp
Friday, January 23, 2009
PSSA Math Reporting Categories: A Numbers and Operations √ B Measurement √ C Geometry D Algebraic Concepts E Data Analysis and Probability SOLUTION Name (legibly printed): _______________________________________________ Seminar (circle one): Ackerman Beals Capers Harvey Hickson Instructions: • Place your solution into box in front of main office by end of 4th period today. • Winner will be announced during 6th period lunch today. Winner will be randomly selected from all entries, but the answer must be correct and justified (SHOW WORK). • Link with questions and solutions posted at http://hopecharter.blogspot.com
How many cubes, 2cm on a side, can be packed into this box?
Note: figure not drawn to scale A B C D
100 120 240 960
Solution: The volume of the right rectangular prism (box) is
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(12 cm )(10 cm )(8 cm ) = 960 cm3
If 1 cm cubes are used to fill the box, then each 1 cm cube occupies (1 cm )(1 cm )(1 cm ) = 1 cm3
⎛ 1 cube ⎞ . that is ⎜ 3 ⎟ ⎝ 1 cm ⎠ Using dimensional analysis (make units cancel): ⎛ 1 cube ⎞ 960 cm3 ⎜⎜ ⎟ = 960 cubes 3 ⎟ ⎝ 1 cm ⎠ Therefore it would take 960 cubes that are 1cm x 1cm x 1cm to fill the 960 cm3 box.
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Likewise, if 2 cm cubes are used to fill the box, then each 2 cm cube occupies ( 2 cm )( 2 cm )( 2 cm ) = 8 cm3 ⎛ 1 cube ⎞ that is ⎜ . 3 ⎟ ⎝ 8 cm ⎠ Using dimensional analysis (make units cancel): ⎛ 1 cube ⎞ 960 cm3 ⎜⎜ ⎟ = 120 cubes 3 ⎟ 8 cm ⎝ ⎠ Therefore it would take 120 cubes that are 2cm x 2cm x 2cm to fill the 960 cm3 box Æ Answer is B
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