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 theSAT Operating System for TI-89 and TI-89 Titanium graphing calculators and just 5 minutes of your time, you can ...
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