SAT Math Sample Problem: Diameter of a Sphere - SAT Operating System Application Tutorial

ORIGINAL TEXT: 8) A cube with surface area of 54 sq. inches is inscribed in a sphere. If each vertex of the cube touches the sphere, what is the length, in inches, of the diameter of the sphere? We can solve this problem with the SAT Operating System directly! This is how we work out the logic of the problem before we use the SAT Operating System: 1. We have the surface area of the cube (54 sq. in). 2. We know that each vertex of the cube touches the sphere. That means that we want to find the diagonal of the cube. To do this, we will need to use the Pythagorean Theorem twice. Once to find the diagonal of the base of a triangle and then a second time to find the hypotenuse of a triangle which will be the diagonal of the cube. That diagonal of the cube is the same value as the diameter of the circumscribed sphere. Answer: 1. For step one, we found the side to be 3 (can't be negative 3 since dimensions are not negative) 2. For the diagonal of the bottom face of the cube, the value is: 4.2426 3. For the diagonal of the whole cube: Use 3 for one side, 4.2426 for the base, and we found the diagonal of the cube (the hypotenuse) to be: 5.19612 ANSWER: Thus, the diameter of the sphere is: 5.19612 Now, your answer choices may not be in decimal format, so compute each answer choice if it's in fractional format to get the decimal form of the value. ------------- With the SAT Operating System for TI-89 and TI-89 Titanium graphing calculators and just 5 minutes of your time, you can raise your SAT score by over 60 points (on average)! In this video, we show you exactly how to apply the software to solve a REAL SAT math problem. To download the software, please visit: http://calc-tech.com. For more sample problems like this, please visit our YouTube channel (   / calctechllc  ) If you have any questions, please send us an email at: [email protected]. Good luck on your SATs! All trademarks are the property of their respective owners. *SAT is a registered trademark of the College Entrance Examination Board, which was not involved in the production of, and does not endorse, this web site. *PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation, which were not involved in the production of, and does not endorse, this web site. SOURCE: http://answers.yahoo.com/question/ind...